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Class~fiC \ O ft 
Book ■( — 14" 
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COPYRIGHT DEPOSIT; 



<?iyjc- 



ELEMENTS OF LOGIC; 



DESIGNED AS A 



"So 



MANUAL OF INSTRUCTION. 






BY 



V 



HENRY COPPEE, LL.D. 

PRESIDENT OF THE LEHIGH UNIVERSITY. 



REVISED EDITION. 



PHILADELPHIA: 
E. H. BUTLER & COMPANY. 

1872. 



^c 



4" 



.01 



Entered according to Act of Congress, in the year 1857, by 

E. H. BUTLER & CO., 

In the Clerk's Office of the District Court of the United States in and for the 
Eastern District of Pennsylvania. 



Entered according to Act of Congress, in the year 1872, by 

E. H. BUTLER & CO., 
In the Office of the Librarian of Congress, at Washington. 



LC Control Number 




tmp96 025789 



WestcottA Thomson, Sherman & Co.. 

Stereotypers, Philada. Printers, Philada. 



PREFACE 

TO THE REVISED EDITION. 



In obedience to the public demand, the publishers have 
spared no expense in giving to this volume a new and 
more attractive form. The author has, on his part, re- 
vised it carefully, and added much important matter, some 
of it embodying the valuable suggestions of instructors 
who have been using it for many years. Parts of the 
subject have received fuller illustration. Parts have, after 
careful deliberation, been omitted, and a chapter has been 
added on the Fundamental Laws of Thought or First 
Principles of Reason. The plan and divisions of the 
work remain the same. As many and apparently conflict- 
ing views have been taken of the meaning, genus and 
scope of Logic, as a branch of Philosophy, it seems proper 
to say that much of the diversity is nominal ; that, with 
differences in name, most treatises admit the same func- 
tions of words, conceptions, propositions and arguments, 
and that the chief antagonism arises from an undue exag- 
geration of the place and value of certain functions in the 
reasoning process. This remark is made in the interest 
of those who are deterred by the apparent antagonism of 
systems from the study of a science most of the details 



4 PREFACE TO THE REVISED EDITION". 

of which are the same in all systems ; the body of logical 
doctrines recognized by all logicians do not refuse to com- 
bine harmoniously in one system. 

In the present edition the author has availed himself 
of the voluminous and exhaustive treatise of Sir William 
Hamilton, in which, together with the expression of his 
peculiar views and criticisms, some of which may be dis- 
sented from, the functions and the history of Logic have 
been set forth with great acuteness and erudition. This 
has led the author to slight modifications of the system 
of Whately, but none that will affect the general import- 
ance and soundness of his views. The numerous more 
recent treatises on the science have also been examined. 

It is confidently hoped by the author and the pub- 
lishers that the favor so continuously displayed towards 
this work ever since its appearance fifteen years ago will 
be increased by its additional value and its clear and 
attractive form ; and that a subject frequently regarded as 
both abstruse and vague will be commended, by the clear- 
ness and simplicity of its treatment, to many who have 
been heretofore doubtful of its utility. 

H. C. 

The Lehigh University, August 1, 1872. 



PREFACE 

TO THE FIEST EDITION. 



The following treatise has been written in the hope 
that it may supply, in some degree, a real want. For 
several years the author was a teacher of Logic in the 
Military Academy at West Point, where the subject was 
thoroughly studied by the aid of Archbishop Whately's 
text-book. 

How much a manual was needed before that work 
appeared may be known, from the significant fact that, 
as soon as it was published as an article in the Ency- 
clopedia Metropolitana, it was eagerly caught at by the 
community of teachers, and. used, unaltered, as a book 
for college instruction, on both sides of the Atlantic. 

Since the publication of that article many have at- 
tempted the preparation of a manual which should have 
the instruction of classes as its original design ; but the 
soundness of Whately's views and the conciseness of his 
expression still gave to his work the greatest circulation. 
Among so many endeavors the author would venture 
to express the hope that his little manual may find its 
special purpose and mission. It is short ; it is explana- 
tory of all the difficult points so often left to confuse a 

1* 5 



6 PREFACE TO THE FIRST EDITION. 

student ; the arrangement is simple, and much that in a 
larger treatise would be 1 of necessity included is here 
omitted, so that what the student learns in the limited 
time of a college term he may learn well, and retain in 
his memory as a basis for further investigations. To 
some persons it may seem too much simplified j but let 
it be remembered that it is a manual for youth, and 
that its only aim is to teach them the Elements of Logic 
as the foundation of all reasoning. 

The basis of the work is " Whately's Logic" ; many of 
the examples are taken directly from that ; so many, in- 
deed, that the acknowledgment is here made for them all, 
and for much that is excellent in arrangement and in 
expression. As the clear expounder of Aristotle, and the 
originator of much that is valuable, Whately must stand 
at the head of the Logicians of this age. The author 
would refer specially also to the material assistance ob- 
tained from " Levey' s Logic" (Bonn's series); "Aristotle's 
Post and Prior Analytics" (Bonn's translation); "Neil's 
Art of Reasoning;" "Blakely's Historical Sketch of Logic;" 
"Lord Bacon's New Organon; Arnaidd (Logique de Port 
Royal) ; J. Bentham's "Book of Fallacies." . From Neil a 
few of the examples have been taken. 

Besides these, he has consulted a great number of works, 
the aid derived from which is so general that they do not 
require special mention. 

University of Pennsylvania, July, 1857. 



TABLE OF CONTENTS. 



CHAPTEE I. 



Logic, the Meaning op the Teem, and the Scope of the 
Science. 

PAGE 

Section 1. Of the term Logic 13 

2. Sources of Error 14 

3. Logic. and Philosophy 15 

4. Logic and Ehetoric 17 

5. Objection to Logic as an Art 18 

6. Natural Logic 20 

7. Systematic forms of Error 21 

8. Of Method 22 

9. Analysis and Synthesis , 23 

10. Analysis and Synthesis as applied to Logic , 27 

1. Analytical View. 2. Synthesis 27 

3. Historical Yiew , 28 



CHAPTEE II. 

Analytical Yiew of Logic. 

Section 11. The Eeasoning process Analyzed 29 

The Dictum of Aristotle.. 31 

CHAPTEE ILL 

A Synthesis of Logic. 

Section 12. Of certain operations and states of the Mind used in 

the process of Argument „. 35 

7 



TABLE OF CONTENTS. 

PAGE 

1. Apprehension . 35 

2. Judgment 36 

3. Seasoning 37 



CHAPTEE IV. 

Section 13. Of Terms 39 

14. Division of Simple Terms 40 

15. Quantity and Quality of Terms 42 



CHAPTEE V. 

Or those Operations which Eelate to Terms. 

Section 16. Abstraction and Generalization 44 

17. Species, Genus and Differentia 45 

18. Property and Accident 47 

19. Of the different orders of Genera and Species 48 

20. Eealism and Nominalism „ 50 

21. Definition of Terms 51 

22. Nominal and Eeal Definitions 53 

23. Eules for Definition 54 

24. Division 58 

25. Eecapitulation 62 



CHAPTEE VI. 

Section 26. Propositions 63 

27. Simple and Compound 66 

28. Quantity and Quality of Propositions 67 

29. Of the Distribution of Terms in Propositions 70 

30. Conversion 73 

Illative Conversion — 76 

31. Of Opposition 78 

32. Of the Matter of Propositions , 79 

33. Of Compound Propositions 81 

34. The New Analytic 84 



TABLE OF CONTENTS. 9 

CHAPTEE VII. 

PAGE 

Section 35. Of Arguments 87 

36. Of the Syllogism 88 

37. Logical Axioms. , 89 



CHAPTEE VIII. 

Of Figure and Moods. 

Section 38. Figure.. 95 

39. Mood 98 

40. Of Eeduction 107 

41. Indirect Eeduction Ill 

42. dotation of the Syllogism 113 

CHAPTEE VLX. 
Of Irregular, Informal and Compound Arguments. 

Section 43. Of Abridged Syllogisms 118 

44. The Sorites 121 

45. The Epichirema 124 

46. Of Hypothetical Syllogisms 126 

Conditional 126 

Disjunctive 130 

The Dilemma 132 

CHAPTEE X. 

Fallacies. 

Section 47. The Meaning and Comprehension of a Fallacy 137 

48. Fallacies in dictione 138 

49. Material or Informal Fallacies 141 

Errors in the Premisses 142 

Petitio Principii 142 

Arguing in a Circle 142 

Non causa pro causa 143 

Errors in the conclusion , 145 



10 TABLE OF CONTENTS. 

PAGE 

Irrelevant conclusion 145 

Argumentum ad rem, etc 148 

Changing the point in dispute 148 

Fallacy of Objections , 149 

50. Verbal Fallacies 150 

1. Etymology 152 

2. Interrogations 153 

3. Amphibolous Sentences 154 

Causes of Ambiguity 155 

51. The manner of removing Ambiguity , 160 

52. The Fallacy of Probabilities 161 

53. Popular Fallacies 163 



CHAPTEE XI. 

The Fundamental Laws^of Thought or First Principles 
op Reason. 

1. Identity 167 

2. Contradiction 168 

3. Excluded Middle , 168 

4. Reason and Consequent 168 



CHAPTER XII. 

Section 54. Of certain modes in which Logic is applied 173 

Intuition, Induction, Deduction...., 173 

Argument a priori, a posteriori, a fortiori 176-178 

The Investigation and Discovery of Truth 178 

1. Observation 179 

2. Hypothesis 179 

3. Induction 179 

4. Theory 180 

Of the Nature and Kinds of Evidence 180 

Consciousness 180 

Sensation , 180 

Analogy 181 

Induction 181 

Testimony ,.... 181 



TABLE OF CONTENTS. 11 

CHAPTER XIII. 
A Historical Sketch of Logic. 

PAGE 

Section 55. Division of the Subject 182 

1. Aristotle. 2. Christianity and Logic. 3. Bacon 
and the rise of Inductive Science. 4. The Present 
System. 

56. Aristotle 184 

The Categories 188 

57. The Logic of Christianity 193 

58. The Logic of Experimental Philosophy 200 

59. Logic in the 18th and 19th centuries 209 

60. Categories and Classification...., 211 

61. Conclusion 217 

APPENDIX. 
Examples for Praxis , 218 



LOGIC 



CHAPTER I. 

LOGIC: THE MEANING OF THE TERM AND THE SCOPE 
OF THE SCIENCE. 

(1.) Of the Term Logic. 

Logic is directly from the Greek Aoyr/.rj, feminine of the 
adjective Xoyr/.og, and implies ^ruaryj [i-q or riyvt] — science or art. 
The adjective is from the noun logos. As, of all the Greek 
words which have been transferred to our English speech, 
none is vaguer and more subtle in its meaning than the word 
logos (Xoyoq), so, of all the sciences, none has been less clearly 
defined, both as to its meaning and its scope, than the science 
of Logic, the name of which is taken from that word ; and, in 
consequence, no term is more erroneously applied and more 
frequently misapplied than the name itself. 

Logos means both thought and speech, and the earlier writers 
distinguish it as being both that in the mind and that without. 
Combining these, logos came to mean discourse, and hence 
some writers have supposed Logic to be simply the science of 
spoken or written language, thus confounding it, in part, with 
Rhetoric, and even with Grammar; others, considering dis- 
course to imply not simply the written symbol or the spolcen 
sound, but also the expression of the thought, have more cor- 
rectly supposed Logic to be the Science of the Laws of Thought, 
and, as such, a branch of metaphysics, or the science which 
investigates the workings of the mind ; others still, and by far 
2 13 



14 LOGIC. 

the greater number, regarding it as a union of language and 
thought in the deduction of truth, have claimed that it had 
to do with the subject-matter of scientific investigation, and 
have thus erred more widely than all by confounding Logic 
with the labors of physical, metaphysical and ethical philoso- 
phy rather than an instrument for the service of them all, as 
it really is. 

It seems necessary, then, at the beginning of a treatise on 
this subject, to define the meaning of the word, and the true 
scope of the science, before we undertake its study — to rid 
ourselves, as it were, of the mists which surround us, before 
we can even see clearly the field in which we are to labor. 

(2.) Sources of Error. 

Many accurate thinkers have confused the minds of stu- 
dents by producing books which, while they contain a just 
view of the logical system itself, attempt at every step, as has 
been said, to explain the subject-matter upon which this system 
is employed, and which forms no part of it; while many 
others, adopting strongly the views of those who have initiated 
so-called systems of logic, have, as partisans, carried forward 
from period to period old errors and old perplexities ; and, 
themselves ignorant of the subtleties which surround them, 
have called their views the true logic, and those of every other 
writer false. Others again have endeavored, in an amiable 
but unscientific spirit, to harmonize all the schemes of the 
philosophers, and to call the result, full of error and inexact- 
ness, the system of Logic. 

There are, indeed, in the systems of the great philosophers 
many parts that are mutually dependent, and true science 
will be found to harmonize with itself everywhere. But since 
there is also error in them all, no mere greatness of name 
should exempt from the scrutiny and exposure of error. 

We must take care to distinguish between the different 
functions of the intellect, so as to call things by their right 



LOGIC AND PHILOSOPHY. 15 

names — not including in the name Logic what belongs to 
Physics or Metaphysics, but laying down at the outset the 
limits and province of that system which we wish to designate 
by the word Logic. If we can do this we shall have accom- 
plished very much at the beginning, and shall find our labor 
easy as we proceed. s 

If we would see how important it is rightly to understand 
this fact of the ambiguity of the word Logic, as frequently 
employed, w T e need but look for a moment at the errors into 
which modern philosophers have fallen when speaking of the 
Logic of Aristotle as compared with the Logic of Bacon. 
This has been fostered by the fact that w T hile Aristotle set 
forth his logical views in his Organon, Bacon produced a 
Novum organum or new organon. If, as w r e shall endeavor to 
demonstrate, Logic is the science which controls the universal 
and ultimate principle of reasoning, given to man, just as 
speech w T as given to him, by a beneficent Creator, then it is 
not Aristotle's Logic, nor Bacon's Logic, but a single universal 
Logic, given to man as the rule of his reason, which must be 
intelligible and harmonious wherever and by whomever it is 
used. 

(3.) Logic and Philosophy. 

In this consideration another word plays a prominent part. 
The word which has been pressed into service, to denote the 
peculiar progress of great minds in the domains of Truth, is 
"Philosophy ;" but even the word "Philosopher," said to be 
adopted by a wise ancient* as a more modest title than aoifwq, 
as the sages of Greece were called, has been productive of 
great confusion. "Philosophy" has been made to stand for 
a thousand sciences, and to preside in the kingdoms of mind, 
morals, and physics, until to be a philosopher means to pursue 
one of many intellectual pursuits, and Philosophy unqualified 
means everything or nothing. 

* Pythagoras. 



16 LOGIC. 

And yet this vague and inexact term Philosophy is 
the one which has been most frequently confounded with 
Logic, and a want of clear definition and of a just under- 
standing in the dispute has led to the production of in- 
exact, distorted, and conflicting systems, both of Philosophy 
and Logic, which have confused those desirous of learning, 
and deterred many from the difficult and perilous attempt. 
In attempting to reach a clear division and definition of 
Philosophy and Logic, the followers of Plato asserted 
Logic to be a part— and the instrument — of Philosophy. 
The Stoics divided Philosophy into three parts, viz. : 
Physics or Theoretical philosophy; Ethics or Practical 
philosophy, and Logic, a subsidiary part, instrumental to 
the others. 

Indeed both words, and the errors to which their use has 
led, indicate, at once, the yearning and the weakness of the 
human mind — the desire of man to investigate and systema- 
tize truth, combined with the obscurity and doubt which 
beset his investigations at every step. 

The acuteness of the Greeks, upon which had been grafted 
all the j)ower and attainment of the Oriental world, could 
reach no clearer nomenclature than to call their studies and 
their inductions Philosophy — the love rather than the attain- 
ment of wisdom — and the art by which they reasoned from 
truth to truth, by which they progressed from parallel to par- 
allel in the sea of doubt and uncertainty, Logic, the art of 
words or discourse, the very mention of which suggests a 
dubious question, and calls up, as it were, two opponents in 
considering it. 

Without considering the numerous definitions, we may 
agree to call Philosophy a search for final causes, in accord- 
ance with a primary law of the mind, which demands a caui-fe 
for everything, and also in obedience to the tendency of all 
science to unity. This covers the investigation of truth as 
to its subject matter; the processes of collating and com- 



LOGIC AND RHETOEIC. 17 

paring material, and of classifying and aggregating observa- 
tions and experiments. 

Logic we shall consider the science which guides the ope- 
ration of thought from simple intuitions and conceptions, 
through judgments, to the simple reasoning process, by which 
we pass from truth to truth already found, and by which we 
guard against fallacious arguments in the passage. 

(4.) Logic and Rhetoric. 

The exact line between Logic and Rhetoric is not always 
clearly drawn. The distinction between them may be thus 
stated : Rhetoric is the art of inventing, arranging and ex- 
pressing thought in discourse, or, in brief, it is the Art of Dis- 
course. Rhetoric finds terms, propositions and arguments ih 
the construction of discourse, and arranges and clothes them 
with language to produce a certain effect. 

It is the province of Logic to test the Rhetorical operations, 
and particularly to declare of its arguments whether they are 
valid or invalid. Thus, in its relation to Rhetoric, Logic is a 
check and an ordeal ; an arbiter of the reason ; a detecter of 
what is false and fallacious. 

In this view Rhetoric includes Grammar. Thus a dis- 
course may be grammatically correct, and rhetorically ele- 
gant, and yet full of error as to its Logic. 

Having thus seen that the name Logic is in a great degree 
arbitrary, and that we should not attain to an understanding 
of the subject, if we followed, even remotely, the etymology 
of the word, we repeat that Logic has to do neither with the 
words themselves — except as they are arranged into terms, 
propositions and arguments — nor with their meanings, except 
as related to reasoning, i. e., passing from two known and ac- 
hioicledged judgments to a third, which is derived from their com- 
bination. With this explanation, then, we may state the defi- 
nition of the term. Logic is the Science and tJie Art of Rea- 
soning ; and reasoning is the ultimate process of thought in 
2 * B 



18 LOGIC. 

its search for the True, the end proposed to us by our cogni- 
tive faculties. 

Of these two terms, Scienee and Art, we remark that Art is 
in a critical sense more extensive than Science, since the prac- 
tice of an Art implies the application of the principles of 
Science, while, on the other hand, Science might, indeed does, 
exist in its theoretic state without being put to practical use. 
The Science would be the investigation of the principles upon 
which the human mind is based in reasoning, and the Art the 
application of those principles to the establishment of prac- 
tical rules for conducting the process. Logic may then be 
more simply defined the Art of Reasoning, and as such we 
shall consider it in these pages, less concerned about the 
composition of man's reason than about the practical laws 
and methods by which it works. 

Before proceeding to explain the system of Logic, which 
has developed itself since the days of Aristotle, let us meet 
at the threshold some plausible objections which have been 
brought against the establishment of any system whatever. 

(5.) Objection to Logic as an Art. 

As man has been universally gifted with reason, by means 
of which he may combine his thoughts and arrive at just 
conclusions, and with language in which to communicate 
them, it is asserted that every man carries his own Logic 
within him, as the immediate gift of God. 

All men reason, it is true, and many men are not aware of 
the logical process which they use ; and this has been made, 
even by men of acute minds, an objection against Logic ; for, 
they say, since men reason, and reason well, without rules, 
and without knowing the process, a system of rules must be 
unnecessary. 

The objection is plausible, arid has been fruitful of evil. 
But as it is one which may be brought against many other 
arts as well as Logic, it may, we think, be most easily met 



OBJECTION TO LOGIC AS AN AET. 19 

and most clearly refuted by illustration. Many children 
speak with correctness and precision before they have any 
knowledge of Grammar ; and there are persons of wonderful 
powers in arithmetical computation who have never learned 
Arithmetic; but Grammar and Arithmetic are not for such 
reasons condemned : their rules are an infallible test for pre- 
cise speaking and correct computation, and are thus guides to 
the weaker and slower intellects — and these constitute the 
immense majority of mankind — to keep them from formal 
error. So, too, in Music and Painting ; great geniuses arise 
in both Arts, but no one would contend that hard study, ac- 
cording to the established systems of the great composers and 
the great masters — established upon the true principle of 
voice and ear and eye — is not absolutely requisite to excel- 
lence and success. 

Many persous of clear perceptive faculties, and who form 
and combine their judgments rapidly, may reason acutely 
and well without a system of rules ; but, in order to be certain 
of their correctness, others must have some invariable test ; 
on the other hand there are many, of quick but erratic minds, 
who reason with such dangerous sophistry that the most deli- 
cate logical tests alone can expose the fallacy, of which in- 
deed they may not themselves be entirely aware. As such 
delicate tests have not been within the reach of the multi- 
tude, it is thus that men have become, for want of a popular 
knowledge of Logic, at once self-deceivers and deluders 
of mankind : have established illooical religious creed?, 
monstrous social fallacies, false theories of government, which 
are immediately made manifest by the simple application of 
Logic. 

Nay, more : since Logic is the science which develops the 
one universal principle of Reasoning, applied alike to every 
branch of science, Exact or Inductive, it seems much more 
necessary that we should establish full and unerring rules for 
our guidance, and thus be kept, at every turn, from the mani- 



20 LOGIC. 

fold errors which arise from systems based upon such objec- 
tions as those we have mentioned. 

(6.) Natural Logic. 

The natural laws which govern the human mind in its 
attempts to reason have been called by the opposers of Logi- 
cal systems Natural Logic. We accept the name, and are 
ready to allow that, in following these laws, reason is right, 
and originally perfect in applying them ; but now, in the fallen 
condition of man, reason is certainly liable to be biased by 
prejudice, distorted by passion, or insidiously tempted into 
open error. Thus many men, who reason correctly on most 
subjects, are swayed, in one or more, by self-interest, partisan- 
ship, fashion, predominance of the imagination, and such like 
causes ; and thus men of equally clear minds in the main, 
from the same premises draw different conclusions, or estab- 
lish the same conclusion by very different premises. Thus 
also the same man, at different periods of his life, or swayed 
by various circumstances, will reason differently ; and from 
such causes, it is evident that each man's natural Logic is not 
a sufficient guide for his reason. Besides, reason does not 
confine itself to the immediate conclusion flowing from these 
fundamental laws of reasoning, but is constantly drawing one 
conclusion from another. ]S"ow, in this process, reason cer- 
tainly needs more than these natural laws to keep it from 
error. 

Yet still it is from this natural Logic, or, rather, the con- 
currence of the right reason of many well-ordered minds, that 
the science of Logic has been deduced. 

By a systematic observation of such minds, as they reason, 
taking care to remove all causes of error in each particular 
case, we establish rules for the reason, and are able to detect, 
by the application of these rules to other cases, every falla- 
cious argument resulting from such causes of error. 

There must have been reason before there could be a sys- 



SYSTEMATIC FORMS OF ERROR. 21 

tern of laws to govern it, just as we know there was language 
before Grammar was formed. It was to systematize this 
reason, to methodize this natural Logic, and particularly to 
guard against errors in the use of the reasoning powers, that 
a canon was prepared, and that a complete science of Logic 
has been formed. 

We have spoken in general terms of the confusion and 
error which have grown out of the misapprehension of Logic. 
The more special phases of it are those resulting from an 
attempt to systematize these general erroneous notions. 

(7.) Systematic Forms of Error. 

By a very common misuse of language, we hear such 
phrases as " mathematical reasoning ," " moral reasoning," "syl- 
logistic reasoning, " and "inductive reasoning ;" which would 
lead us to suppose that instead of one there were many kinds 
of reasoning. This is a fruitful source of error. 

These so-called different kinds of reasoning are only appli- 
cations of Logic to different subjects and different habits of 
thought. The Logic in each is the same ; the subject-matter 
alone is different. 

It would seem unnecessary to dwell upon this point, but it 
has been so commonly misunderstood, and the error has been 
so disseminated by professional writers upon Logic, that it 
must be plainly stated and carefully remembered. 

When we speak, then, of a good mathematician, we mean 
one who is able, most surely and rapidly, to apply Logic to the 
investigations of numbers and quantity. When we hear of a 
great theologian, we know that he has amassed much theo- 
logical learning, and has applied Logic to it successfully. So, 
too, with other sciences. 

In general, in whichever of the myriad fields of nature 
and mind ardent votaries may wander, however various the 
stores they may amass, they must all come back with their 
sheaves to the great measuring-centre of Logic, and apply 



22 LOGIC. 

its dicta before they can compute or use their gathered 
gains. 

The value of Logic as a study is manifold. Not only is it 
an infallible test of argument, but it strengthens and disci- 
plines the mind, giving it system and method ; and it has 
established a terminology of universal adoption and applica- 
ble to all its practical adaptations in science. Thus it gives 
uniformity to the investigation of all branches of science. 

(8.) Of Method. 

Method is the order and arrangement of facts to produce a 
certain result ; to establish new truth, to investigate old, and 
to explain and teach both. It is derived from the Greek 
fisffodou, which denotes the way through which we arrive at 
a certain result. Method is employed in every science, and 
plays a specially important part in Logic. 

Whatever steps are taken to make knowledge profitable, to 
reduce theory to practice, and to give clear, distinct and con- 
nected ideas of science, constitute Method. The extension of 
the term Method, it is evident, will differ according to the 
subject to which it is applied. 

The methods of investigation differ slightly for the different 
kinds of science, but may generally be classified under two 
heads, Analysis and Synthesis, of which the former is generally 
used in the private investigation of truth, and the latter for 
the purposes of instruction. 

The successive stages in the discovery, progress and estab- 
lishment of any science are three, viz. : the descriptive, the 
inductive (also called the experimental), and the deductive or 
exact stage. 

As soon as, by the description of a science, the statement 
of its present condition, its wants, its unknown causes, etc., we 
have a just representation of it, we proceed to observation 
and experiment, or induction; and when, by induction, or the 
labored collection of many particular facts and examples, we 



ANALYSIS AND SYNTHESIS. 23 

have established general laics, we may then deduce from them 
any particular fact or facts which it concerns us to know. 

These stages of investigation belong equally to the physical 
and moral sciences, with the slight difference in practice 
that the vagueness and complexity involved in mental, spirit- 
ual and social phenomena, which all belong to the moral 
sciences, require more delicate and subtle agencies to trace 
their laws than those of the natural world around us. 

And the sources of experiment are not at all analogous. 
Here we are surrounded by apparent contradictions. The 
world of nature is changeable and shifting, and yet it is pal- 
pable to our senses ; the laws which govern it are mysterious 
and inscrutable, and yet they are constant ; the moral world, 
which is unchangeable and eternal,- is, when considered or 
examined by unaided reason, vague and obscure, and the 
abstract conclusions to which our inductions lead us, positive 
and incontrovertible as they are, are but few and unsatis- 
factory. 

We shall have occasion to consider the subject of Method 
more in detail hereafter, but at present we design to apply it 
to the consideration of Logic. 

We speak of the method of a single science, or a Method 
which is applied to all — as in that which leads to the Classifi- 
cation of the sciences. In either investigation the division 
of Method into Analysis and Synthesis is a just one, as both 
are used in either process. 

(9.) Analysis and Synthesis. 
To illustrate more clearly the nature of these two processes, 
let us take a familiar example. If we designed to teach a 
person how to make and use some complicated structure, as, 
for example, a ship, and if this person had never seen one, 
the first step in the process would be to show him the ship 
completely built and ready to proceed to sea, fully rigged, 
equipped and manned, that he might take in at a glance its 



24 LOGIC. 

finished appearance, and its ultimate design and use: in a 
word, that he might know what he was to learn to make. 
This would be the first lesson in ship-building. The next 
step would be to show it to him partially dismantled, or, in 
effect, to take it to pieces before his eyes, that he might see 
the parts of which it is composed, and their relative position 
in the structure. 

The third step would be to show him how each part was 
made, and to let him see them all in minute detail lying 
together, according to some system, which should be prepara- 
tory to a reconstruction of the ship. 

This process of successive steps is Analysis* or a dissolu- 
tion of anything into its elements. 

In the investigation of any science, it is of primary import- 
ance. Showing us at first the scope and design of the science, 
by systematic degrees it decomposes it into its elements, and 
prepares us for intelligent study of its many forms. 

This operation shows us also the simplicity of science, and 
is evidently derived from the teachings of nature ; for, while 
there are innumerable forms of animal and vegetable life, the 
analysis of nature which is constantly going on shows but 
few parts or elements in all her works, and great simplicity 
of combination of the same elements in different proportions, 
to produce the most dissimilar forms and results. So all 
the sciences, physical, intellectual, and moral, while they 
assume many and varying forms, are in reality composed of 
a few simple elements of nature or mind, and this their 
analysis displays. 

The analysis of physical science is of course the most exact 
of these processes, in proportion as the things of sense are 
easier to comprehend and fix than those of mind and spirit ; 
in physics, this process of analysis is carried from the grandest 
class, such as kingdoms and high genera, to the observation 
and use of atoms and molecules inconceivably small, which 
* avaXvu — to separate into elements. 



*>! 



ANALYSIS AND SYNTHESIS. 25 

are to constitute the basis-elements of a reconstructing pro- 
cess. Accurate analysis is a work of patient labor. Chance 
experiments have indeed occasionally produced great results, 
but this is an argument for, rather than against, careful 
analysis. Eoger Bacon discovered a fulminating powder 
when he was not seeking it ; but, to be useful, this powder 
must cease to be a chance discovery ; that is, it must be ana- 
lyzed into nitre, charcoal, and brimstone, so that, these con- 
stituents once known, we can make our fulminating powder 
at will. Science has never proceeded upon chance ; it moves 
safely only when it moves by invariable but ever-extending 
laws. 

Incomplete analysis has done more to establish and per- 
petuate error than even blind superstition. For it was in 
the face of the latter that Copernicus and Galileo established 
the true theory of the heliocentric system ; while, before their 
time, the incomplete, false, and arbitrary analysis of astron- 
omy, and the belief in stellar influences, which a just anal- 
ysis would have destroyed, led all the writers, from the time 
of Ptolemy, to build a false system of celestial mechanics, 
and thus to clog the wheels of true science. 

The process of analysis having been completed, we come 
naturally to Synthesis* 

Having taken to pieces, we proceed to the other task of 
rebuilding : carefully examining each different element as 
they all lie before us, until we understand thoroughly the 
material of which it is made and its construction, we proceed 
to adjust it to its place in the structure; piece by piece, per- 
haps slowly and painfully, we build the ship, until at length 
it is complete ; nor is the labor yet finished : we launch it 
upon the waters, spread its sails to the wind, and see it in 
practical and successful movement, and then we may account 
ourselves acquainted with the structure, and able to build its 
like whenever called upon to do so. 

* awrifhjfii — to place together. 
3 



26 LOGIC. 

This operation is called Synthesis ; it is evident that it is 
also continually going on in nature in the reproduction out 
of crude materials of the many forms of complicated existence. 

Many writers, in investigating a science, begin with this 
latter process, entirely neglecting the former; but it is so 
evident that the analysis of a science gives large and valuable 
lessons preparatory to its synthesis, or real study for ourselves, 
that most modern treatises on science have adopted and fol- 
lowed this order of instruction. It may then be safely stated 
that in any science the true synthesis can only be proportional 
to a vigorous and just analysis, and there have consequently 
been rules laid down for proceeding to consider any science 
or art in pursuance of this method. 

The rules for Analysis may be reduced to these : 

1st. Not to believe any general scientific statement without 
proof; that proof determined by the just principles of evi- 
dence. 

2d. To divide every scientific dictum into as many parts or 
elements as shall be necessary to resolve it. 

3d. To make a methodical arrangement of these elements 
in order that we may understand them clearly and the rela- 
tion which they bear to each other. 

Having done this, the corresponding rules for Synthesis 
are : 

1st. To use such terms to express the elementary parts as 
are free from ambiguity. 

2d. In combining these, to assume only such clear princi- 
ples or axioms as cannot be contested by any persons. 

3d. To prove, by demonstration, all the conclusions at 
which we arrive, in the employment of the terms and axioms 
used. 

These remarks upon analysis and synthesis, as the two vital 
functions of Method in investigation, and as the two necessary 
instruments of all scientific study, are designed for general 
application. A proper and constant application of the rules 



ANALYSIS AND SYNTHESIS AS APPLIED TO LOGIC. 27 

of analysis and synthesis would cause great advancement in 
our studies, aud would go far to insure us from error, however 
rapid that advancement might be. Analysis and synthesis 
are conducted by means of abstraction, generalization, defin- 
ition and division, which will be referred to hereafter. We 
have placed the subject of Method in this place, because we 
design to use it in application to the study of Logic itself; for, 
as a science to be studied, Logic comes under the rules which 
have been just laid down. 

(10.) Analysis and Synthesis as applied to Logic. 

Now, let us employ this method in investigating the science 
of Logic. 

Abstract or formal logic is an explication of the laws of 
thought and the rules of reasoning, without regard to any 
subject-matter. Applied logic is the application of these rules 
to the subject-matter of scientific investigation. It is only 
with the first of these that we at present have to do. 

That we may study the subject profitably, making each 
step a preliminary to the due understanding of the successive 
steps, we propose to divide the entire subject into the follow- 
ing special considerations : 

1. An Analytical View of Logic. 

In this we regard the science in its aim and its workings, 
and after thus showing its design and its scope, we analyze or 
dissolve it into its different parts, showing what those parts 
are which effect by their combination the purpose designed. 

2. A Synthesis of Formal Logic. 

As Synthesis is the reverse process of Analysis, and as an 
Analysis of such a study would be in reality but a general 
view of the scope of that science which Synthesis is to estab- 
lish, w T e shall see that while our analytical view of Logic may 
be brief and general, our synthesis must be minute and care- 



28 LOGIC. 

ful. We must more particularly examine those parts which 
our analysis has given us, in order that we may be able duly 
to combine them in their just relations. 

In imparting instruction upon subjects which are known, 
the synthesis is evidently the more important process, and 
hence must be longer and more minute, while in the inves- 
tigations of an unknown science the analysis is the more 
important and valuable process. 

In the general synthesis of Logic we shall also devote a 
chapter to the subject of Fallacies, and then consider some 
of the ways in which the syllogism is used, and the technical 
phrases which express these uses. 

3. A Historical View of Logic. 

This historical view of Logic has been placed after the 
study of the formal Logic, rather than before it, as is usual 
in most treatises, because we can appreciate a history only of 
that which we know, and we shall understand much better 
the causes of error and the obstacles to science which history 
gives us when we are beforehand aware of the true scope and 
relations of the particular science whose history is related. 
When we know what Logic is, its history is intelligible and 
interesting, and not otherwise. 

For Logic is so intermingled, or rather entangled, with 
other kinds of philosophy in almost all of its principal 
epochs, that any one who should undertake to read of its 
adventures in history, without being able constantly to dis- 
sociate it from its companion sciences, would find it a useless 
and unprofitable task. 



CHAPTEE II. 

ANALYTICAL VIEW OF LOGIC. 

(11.) The Reasoning Process Analyzed. 

To apply the method of analysis to the study of Logic as 
an art, we begin with the definition already laid down that 
Logic is the Art of Reasoning. 

Reasoning consists in the combination of two known judg- 
ments to form a third, which is deduced from them. Rea- 
soning, when expressed in language, is called argument. 

The ultimate and simple form of argument, logically ex- 
pressed, is the syllogism* In a more extended sense, reason- 
ing • covers also the combination and succession of many 
arguments. 

The syllogism is an argument consisting of three proposi- 
tions, of which the first is called the major premiss, the sec- 
cond the minor premiss, and the third the conclusion. This 
is the usual order of the premisses, but the reasoning would 
be equally valid were they transposed. 

Major premiss. All A is B = All men are mortal. 
Minor premiss. All C is A = All Hindoos are men. 
Conclusion. Therefore all C is B = All Hindoos are mortal. 



Each of these ywopositions consists of two terms, the 
and the predicate; and the verb uniting them is called the 
copula. Men reason to satisfy their own minds, to demon- 
strate truths, or to refute error, and, in so doing, they com- 
bine many of these syllogisms, thus forming compound argu- 
ments, which may always be analyzed into the simple argu- 
ments which compose them. In a simple syllogism, in many 

* aw and 'Tioyifyftai, more remotely teyo. 
3* 29 



30 LOGIC. 

cases, one or other of these premisses conveys a fact so well 
known that it may be taken for granted, and so it is sup- 
pressed, and thus is formed an abridged argument, called an 
enthymeme. For example: 

{Minor premiss) Caesar was a man, 
Therefore Csesar was mortal. 

This is an enthymeme with the major premiss suppressed. 
This major premiss is, All men are mortal, which is taken for 
granted in the conclusion, where, because Ccesar was a man, 
it is affirmed that he was mortal. In every case, however, if 
the enthymene appear at all doubtful, the suppressed premiss 
may be written out, and the validity or invalidity of the argu- 
ment thus determined. Compound arguments, instead of hav- 
ing each syllogism fully expressed, are usually formed of a 
number of enthymemes combined. 

The groundwork of the syllogism is the dictum of Aristotle, 
or his universal test for Argument. 

Without in this place entering even very briefly into the 
History of Logic — a history of experiment and error— it is 
interesting to know the time of its first decided manifestation, 
and the person to whom we owe it as a definite science. In 
that magnificent period when the school of Plato had prepared 
the mind of Greece for the coming of Aristotle, and the 
energy of Philip had opened the way for the conquests of 
Alexander, that system of Logic was formed, which, after 
having passed through the fiercest ordeals, has remained 
almost without change to our day. It has been indeed cov- 
ered up, and to all appearance lost, in the times of European 
bigotry and ignorance; schoolmen and churchmen have 
alike assailed it ; but, with the vital principle of truth, it has 
remained untouched by the ruinous hand of Time, amid 
exploded systems of Ethics, false speculations of Philosophy, 
and the cunning allegories of Heathen mythology. The 
Analytics of Aristotle form the cyclopaedia of Logic in this 
age, as in all former periods. 



THE DICTUM OF ARISTOTLE. 



31 



After many years of patient investigation Aristotle estab- 
lished the "Dictum de omni et nullo" of which the first part, 
de omni, refers to all affirmative reasoning, and the second, 
de nullo, to all negative reasoning. Stated by the use of 
ordinary symbols it would be written as follows : 



The Dictum of Aristotle. 



De omni. 
All A is B. 

(1) (2) 

All or some C is A. 

(1) (2) 

Therefore all or some C is B. 

. (2) 

is not B. 



De nullo. 
No A is B. 
(1) (2) 
All or some C is A. 

(1) 
Therefore no C is B, or some C 



Writing out the forms separately, we have — 
Be omni. 



(1) 




All A is 


B. 


All C is 


A. 


All C is 


B. 


(3) 




No A is 


B. 


All C is 


A. 


No-Cis 


B. 



De nullo. 



Or, if stated by a geometrical notation, as all syllogisms 
may be stated : 

1 2 



(2) 


All A is B. 


Some C is A. 


Some C is B. 


(4) 


No A is B. 


Some C is A. 


Some C is not B. 





But to explain the dictum practically, it has been trans- 
lated thus : 



32 LOGIC. 

Wliatever may be predicated of d whole class, may also be 
predicated of all or any of the individuals contained in that 
class. 

To predicate * means to affirm or deny. 

Thus in the dictum de omni. In the major premiss we 
predicate or affirm B of the whole class A. 

In the minor premiss we assert that all or some C is an 
individual or a number of individuals included under the 
class A. 

And in the conclusion we predicate B of the individuals, 
as we did in the major premiss of the whole class to which 
they belong. 

This simple dictum of Aristotle is the groundwork of the 
syllogism, and the syllogism is the universal principle of rea- 
soning. It is sufficient in this place to state the fact ; it will 
be proven hereafter. The propositions of which the syllo- 
gism is composed are further analyzed. A proposition con- 
sists of two terms and a copula, of which the first term is 
called the subject, the last the predicate, and the connection 
between them is the copula. 

subj. cop. predic. 

(Men) (are) (mortal) 

subj. cop. pred. 

(Men) (are not) (trees) 

It has been said that the dictum of Aristotle is the ground- 
work of the syllogism, and that the syllogism is the universal 
principle of reasoning: it must be also remarked that every 
valid argument, no matter what may be its original form, 
may be put under the form of the syllogism, and to it in that 
form the dictum may be directly applied ; and, on the other 
hand, if any argument cannot be reduced to this form, it is 
invalid. Thus this dictum forms not only the vehicle of cor- 
rect reasoning, but is a sure test of error in Logic. We shall 
* Prcedico — are. 



THE DICTUM OF ARISTOTLE. 33 

constantly recur, in considering every form of argument, to 
this test. 

The reasons why in mathematical investigation we use let- 
ters, and in arithmetic numbers, are — first, to expedite and 
simplify the work, and secondly, to generalize it. For the 
same purposes we use symbols in Logic. If, for example, I 
write the syllogism 

All good men are happy ; 
John is a good man, 
Therefore, John is happy, 

I limit my argument entirely to the particular of John being 
a good man and being happy, whereas, if I write 

All A is B ; 
C is A, 
Therefore, C is B, 

I propose a general formula which will apply to many 
cases according to the subject and the matter of inquiry. It 
will be well for the student to frame particular examples 
under the general formula, and thus at once to fix the form 
in the mind and accustom himself to the practical applica- 
tions of the system of Logic to particular cases. 

Besides the dictum of Aristotle, to the form of which every 
valid argument may be reduced, there will be given hereafter 
a series of rules for detecting fallacy and for determining the 
validity of an argument when it is not exactly in this form, 
and, by means of these, the logical student may defend him- 
self against the subtlest sophistry, holding Aristotle's dictum 
in reserve as a final test. Where one who is ignorant of Logic 
is obliged to use much effort and circumlocution to determine 
the validity or invalidity of an argument, and is in great dan- 
ger of error in the process, the logician, at once and without 
inquiry into the subject-matter of discourse, applies his tests 
to the framework of the reasoning, and indicates infallibly 

C 



34 LOGIC. 

the defect in the argument. And so deciding as to the valid- 
ity or invalidity of the general formula as expressed by the 
symbolical letters A, B, C, he has once for all decided for 
each particular example which can fall under that formula. 

In concluding this brief analysis of Logic, let us recapitu- 
late. Logic is the Art of Reasoning. There is but a single 
universal principle of Reasoning. Reasoning here includes 
the consideration of terms, considered either as intuitions or 
conceptions, their combination by the judgment into propo- 
sitions of various kinds, and the union of propositions into 
arguments as premisses and conclusion. All these processes 
are conducted in accordance with the laws of thought. The 
basis of reasoning is the dictum of Aristotle, and its simple 
form is the syllogism. 

The syllogism is composed of two premisses and a conclu- 
sion; each of these is a proposition, and each proposition 
consists of three parts, two terms and a copula. It is now 
our purpose to examine these constituents of Logical formulae 
in the inverse order, beginning with terms. 



CHAPTER III. 

A SYNTHESIS OF LOGIC. 

(12.) Of certain Operations and States of the Mind in 
the Process of Argument. 

In proceeding to the synthesis of the reasoning process, we 
must first consider certain operations and states through which 
the mind passes in approaching an argument. Logicians 
have enumerated many which are so nearly related to each 
other that we may reduce them to three : 

These are : 1st. Apprehension ; 2d. Judgment ; 3d. Reason- 
ing, or Ratiocination. As a preparation for these in their 
order, Attention has been called the primary state. Attention 
is not a distinct faculty, but an act of will subordinate to 
intelligence — a general phenomenon of intelligence; but this is 
self-evident. Apprehension is a pure conception of an object, 
whether as perceived by the senses or otherwise presented to 
the mental consciousness. The idea or notion of the object 
is the fruit of this operation of the mind. 

By the five senses of the body we have a knowledge of the 
world around us; the first step in obtaining this knowledge 
is sensation, or the impression on the organ of sense; sensation 
is conveyed in a mysterious, inexplicable manner, to the mind, 
to produce perception ; and as soon as we have perceived the 
object by this union between the mind and the senses, the ob- 
ject is apprehended or taken hold of by the mind, and the 
idea is formed or an intelligent knowledge of it is produced. 

Ideas are simple or complex. 

A Simple idea is the notion of one object, or of several 
which bear no relation to each other ; and this notion is ex- 
pressed generally by one word, as John, man, river; or by 

35 



36 LOGIC. 

many connected by conjunctions, John and Peter, the man and 
the boy. 

A Complex idea is the notion we form of several objects 
which bear a relation to each other, as a man walking, a bun- 
dle of rods. 

When an idea produced by an act of Apprehension is ex- 
pressed in language it is called a term. 

But, whereas certain words, which express terms, are equiv- 
ocal or ambiguous, it must be observed that Logic deals only 
with general or abstract terms, and has nothing to do with 
their distinctness or indistinctness. It only takes for granted 
that a term is distinct and unambiguous. A Logical term is 
the expression in language of an idea obtained by act of 
apprehension. 

2. Judgment. 
Judgment is that operation of the mind by which, if we 
have two objects of apprehension or terms, both known to us, 
we declare that they agree or disagree with each other. 
Thus, if I know who "John" is and what "a hero" is, I may 
declare that — 

John is a hero, 
Or that — John is not a hero. 

Judgment is therefore of two kinds — affirmative when the 
two terms are declared to agree, and negative when they are 
declared to disagree. 

An act of Judgment, when expressed in language, is called 
a proposition. 

And here also it must be observed that Logic only takes 
cognizance of abstract propositions, which are expressed by 
logical formulae, and has nothing to do with their truth or 
falsity; or rather, it takes for granted, indeed, that when a 
proposition is stated it is true. 

For example, if the proposition be A is B, it is assumed 
by Logic that A is in reality B, and thus, if, when this gen- 



OPERATIONS OF THE MIND IN REASONING. 37 

eral formula be translated into a particular proposition, it 
prove to be false, Logic is not responsible for the falsehood, 
nor for the error which finds its way into an argument by 
reason of the use of a false premiss. Much error has arisen 
through the mistake of supposing that Logic had to do with 
Language directly, and with the judgments expressed in lan- 
guage ; but it is just such an error as would lead us to assign 
such values to the unknown quantities in any algebraic for- 
mula, such for instance as y 2 — 2px = 0, as would destroy 
the equation. Algebra presupposes the equation to be just, 
and develops only such values of x and y as will establish it. 
The Logical formula is as abstract and general as this, and 
Logical propositions are always assumed as true. 

3. Katiocination. 

Ratiocination is that act of the mind by which, having two 
or more acts of judgment, or propositions, we pass to another 
or others founded upon them and growing out of their com- 
bination. 

Thus, if we have the two propositions 

All men are mortal, 
Ccesar was a man, 

we have, as an inference or fact implied in these two proposi- 
tions, and deduced from their combination, the final proposi- 
tion Ccesar was mortal. 

An act of ratiocination, when expressed in language, is 
called an argument; and an argument, when reduced to its 
simple logical form, is called a syllogism. That simple logical 
form demands a certain order in the premisses and the con- 
clusion. 

If now we examine the syllogism 

Major Premiss. A is B = Men are mortal, 
Minor Premiss. C is A = Csesar is a man, 
Conclusion. C is B = Csesar is mortal, 



38 LOGIC. 

we shall perceive that it consists of three propositions, which 
are called the major and minor premisses and the conclusion, 
and three terms represented by A, B and C, each term being 
used twice in the syllogism. The term which occurs in the 
major premiss and the conclusion (B) is called the major 
term ; that which occurs in the minor premiss and the con- 
clusion (C), the minor term, and that which is found in both 
premisses (A), the middle term. The major term is always 
the predicate of the conclusion, and the minor term the 
subject. 

Extended ratiocination is conducted by the combination 
of many of these syllogisms or their conclusions, according to 
Logical laws. 



CHAPTER IV. 

(13.) Of Terms. 

A term has been defined an idea expressed in language, 
and may be either simple or complex. As we shall see here- 
after, two terms are connected in a proposition, and the name 
is derived from this fact, since they constitute the termini or 
boundaries of a proposition. 

A simple term expresses a single object of apprehension, 
and is generally- one ivord, as man, house, field. 

A complex term is the expression of several objects of 
apprehension with the relation which they sustain to each 
other, as a good boy, a horse running. 

It is evident that the term itself is arbitrary, and of use 
only to convey the apprehension to another, as in different 
languages the terms which express the same object of appre- 
hension will be different words; thus we have the object 
we call horse expressed in French by the word cheval, and 
in Spanish by the word cabdllo. Words, then, it must be 
remembered, are not acts of apprehension, but are arbitrary 
signs for expressing them. 

But language, or the use of words, is necessary to the form 
of reasoning, as no reasoning can be applied and tested until 
it assumes the dress of language. 

When a word is capable of being used alone as a term, it 
is said to be Categorematic* and when it needs the assistance 
of other words to constitute with it a term, it is called Synca- 
tegorematic. Thus man, horse, John, are categorematic words ; 
here, gave, and, are syncategorematic. 

* Karrryopqfia = something alleged or affirmed. 

39 



40 LOGIC. 

By a casual examination of the different parts of speech 
we shall find : 

1st. Of the noun : That it is only categorematic when in 
the nominative case; the possessive, man's, requires another 
word denoting the thing possessed, and the objective a word 
which governs it. 

2d. Of the adjective : That it is syncategorematic ; for, 
although we say John is good, we understand man or boy 
after good. 

3d. Of the verb : That it is, so to speak, more than catego- 
rematic, or hypercategorematic, since it contains often the copula 
and the predicate : as, the man walks ; in this sentence walks 
is equivalent to is walking, in which is is the copula, and 
ivalking the predicate. 

The infinitive mood is often in reality not a verb, but a noun 
in the nominative case. Thus the sentence To die for one's 
country is hapjpiness, means Death for one's country is happi- 
ness ; To die being fully expressed by Death. 

4th. Of the remaining parts of speech we see at a glance 
that they are syncategorematic, and are only used in connec- 
tion with other words to constitute terms. The word which 
has the form of the present participle is sometimes an infinitive, 
and sometimes a noun; we might substitute it in the last 
example given as a case of either. Dying for one's country is 
happiness, is equivalent to both the forms given. 

(14.) Division of Simple Terms. 

Simple terms are divided into singular and common. 

A singular term is that which expresses a single individ- 
ual, and is usually the name of a person, place, or thing; as 
John, Philadelphia, the Delaivare. 

A common term is that which expresses any individual or 
individuals of a whole class ; as a man, the men, an army. 
To make a common term singular, we prefix the demonstra- 
tive pronoun this or that, as this man, that river, which is 
equivalent to stating the name of the man or river ; as, This 



DIVISION OF SIMPLE TEEMS. 41 

man is John; That river is the Delaware. Common terms 
stand for classes, and are sometimes called appellative, as 
giving name or appellation to many individuals. 

They thus are of great aid to science, in that, when many 
common properties have been discovered in a great number 
of individuals, and their distinctive peculiarities have been 
discarded, they may all be called by one name, and that name 
will be a common term ; when this is in view a common term 
is called, according to its comprehension, genus or species. 

Common terms are further distinguished, according to their 
matter, into abstract and concrete. 

An abstract term is an ideal word, expressing an abstract 
property capable of inherence in an object, and yet without 
reference to that object. Thus hardness, length, beauty, are 
abstract terms, which inhere in many objects, but do not indi- 
cate any particular one. 

A concrete term is one which presents to the mind, at once, 
the property and the existence of the object in which it 
inheres. Thus hard, long, beautiful, are concrete terms, im- 
plying certain objects which are hard, long, or beautiful. 

Concrete terms are also called denotative and connotative, 
because they denote the abstract property, while they connote 
or imply in their signification the body or object to which it 
belongs. Thus hardness, being an abstract term, is also an 
ideal noun ; the mind rests upon the vague idea, because it 
indicates nothing farther ; but when hard is mentioned we 
feel the right to ask, what is hard? the answer is — stone. 
Thus the concrete term hard has denoted the quality of hard- 
ness, and connoted stone as the object in which that quality 
inheres. 

Terms are also divided into absolute and relative. An 
absolute term is one which does not refer to any other. 

A relative term is one which refers to or implies another. 
Two terms which have a necessary relation to each other are 
called correlatives. Thus father and son, king and subject, 
brother and sister, are correlatives. Sometimes one term has 

4* 



42 LOGIC. 

several relations, or more than one correlative. Thus nephew 
implies uncle or aunt, and the brotherhood of father or mother 
with sister or brother. 

(15.) Quality and Quantity of Terms. 

Terms are further divided according to their quantity and 
quality. 

The quantity of a term expresses how much of it is taken 
or considered. 

The quality of a term is the mode or manner in which it 
expresses an idea of an object. 

Quality is essential or accidental. An essential quality is 
that without which we cannot conceive of the existence of 
the object; such as sense and intelligence in man; length, 
breadth, and other dimensions in body. 

An accidental quality is one which the object may have at 
one time and not at another ; as whiteness in a wall ; health 
to the body. 

Terms are said to be synonymous under this division, when 
they express the same act of apprehension ; but by common 
usage this exact meaning is departed from, and synonymous 
terms now mean those which express different shades of mean- 
ing ; thus happtiness and felicity are synonymous terms, and 
yet their etymology teaches us a difference in their meanings ; 
the former attributing pleasure to luck or fortune, and the 
latter simply asserting a state of unalloyed pleasure. 

Incompatible terms are those which cannot be used as pre- 
dicates of the same subject at the same time : thus hot and 
cold ; asleep) and awake. 

Positive terms are those which state the real existence of 
the objects they stand for. The opposite of these are nega- 
tive terms, or those which deny the existence or assert the 
absence of certain objects or attributes. 

There is a class of terms called Privative, which are often 
confounded with negative terms ; but there is a real and im- 



QUALITY AND QUANTITY OF TERMS. 43 

portant difference between them. A privative term expresses 
that some quality or attribute usually belonging to the class 
is wanting in some individuals of that class: thus dumb, 
idiotic, are privative terms, since their very names call to the 
mind the fact that man generally is gifted with speech and 
reason, while negative terms denote the absence of a quantity 
or property which is not due to the subject. 

Terms are divided according to their quantity into many 
distinct classes, expressing their number and dimensions. 

Thus we have the common division of numeral and ordi- 
nal, as twenty, a hundred, two ; positive (in its grammatical 
sense), comparative and superlative terms, as good, better, best. 

That which is more truly a logical division is into distributed 
and undistributed : a distributed term being one the whole of 
which is considered, and an undistributed term one of which 
only a part is taken, this part being usually an indefinite part, 
expressed by such words as some, few, several, etc. All men 
is a distributed term, some men an undistributed term. 



CHAPTER V. 

OF THOSE OPERATIONS IN LOGIC WHICH RELATE TO 

TERMS. 

(16.) Abstraction and Generalization. 

Cognitions, Intuitions and Conceptions. — A cognition 
is the impression which an object makes upon our mind, so 
that we know it. 

An intuition is the knowledge or cognition we have of a 
single object, as this house; the State house; John, the Hudson. 
The mind receives an intuition, by simply attending to the 
object. This is a technical use of the word intuition. 

A conception (con and capere) is a notion formed by gather- 
ing several objects into one, as river, man, house. 

Conceptions are formed by the processes of abstraction and 
generalization. 

Abstraction consists in drawing off and considering one or 
more of the properties of an object to the exclusion of the rest. 
Thus we use abstraction when we observe the color and odor 
of the rose, disregarding its other characteristics. If we ab- 
stract the color and odor of one flower, then of another, and 
so of many, and finding these alike for all, call them all by 
one common name Rose, we are said to generalize. Abstrac- 
tion aids us in passing from the confused and complex to the 
distinct — always dividing and simplifying : it is both positive 
and negative, considering one or more by the negation of 
others. 

Generalization, then, consists in disregarding the differ- 
ences between many objects which are alike in certain properties, 
only considering those which are alike and calling them by a 

44 



SPECIES, GENUS AND DIFFERENTIA. 45 

common name — and thus it is that general and universal ideas 
are obtained. 

We may abstract, it is evident, without performing the 
other process of generalizing, but we cannot generalize with- 
out first abstracting : in the general case, however, we abstract 
for the purpose of generalizing. It is by these two processes 
that we obtain common terms, or the names of classes. All these 
common terms are the result of higher or lower processes of 
generalization. Thus, by a low generalization, we obtain tea- 
rose, by a higher, rose, by a higher still, flower, and by one 
step farther, vegetable, etc. But common terms, as classes, are 
further distinguished into species and genera; and, as expres- 
sive of certain things belonging to the species and genus, they 
are also divided into the differentia, property, and accident. 
Some writers, in considering the substance of a term, have 
called the object for which it stands, the essential part or the 
essence. 

A class denoted by a common term may be considered ac- 
cording to its intension or extension. By intension (also called 
comprehension) is meant, the inclusion of fewer objects with 
more specific differences ; and by extension, the inclusion of a 
greater number of objects with fewer specific differences. 
Thus a species has more intension than its genus, the genus 
more extension than its species. 

(17.) Species, Germs and Differentia. 

A species is a class obtained by generalization, which in- 
cludes only individuals or subordinate classes, and is itself 
included in a genus : as an Arabian horse is a species of horse; 
horse is a species of quadruped ; quadruped is a species of ani- 
mal. A genus is a class obtained by a higher generalization, 
which comprehends under it two or more species; as animal 
is the genus alike of quadruped and biped, quadruped is the 
genus of horse, cow, deer, etc., and biped the genus of man, etc. 

It is evident that in one sense the species implies more than 



46 logic. 

the genus ; as, for instance, if quadruped be the genus and 
horse the species, horse will contain all the signification of 
quadruped, and also the distinctive signification of horse as to 
shape, size, habits, uses, etc. ; which latter does not belong to 
quadruped. 

For this reason the species is said to express the whole 
essence of the object, while the genus expresses only apart of 
the essence, and that the material part, or part common to all 
the species under that genus. Thus, man expresses the whole 
or complete essence of the animal so called, while animal 
expresses only the comprehensive or material part of the 
essence which only limits him to an animate existence. 

The differentia of an object is the formal or distinguishing 
part of that object, and divides it from a class to which it 
does not belong ; and when united with the genus or material 
part, or part common to all, forms with it the species, or whole 
essence. Thus, if man be the species, and animal the genus, 

(species) 

rational would be the differentia, and we should have man = 

(differentia) (genus) 

rational animal ; by which it appears that although the ex- 
tension of the genus includes this species and many others, the 
species really comprehends, although in a different sense, more 
than the genus — namely, the genus and differentia — while the 
genus expresses only the material part, or that common to all. 
The genus has greater extension, i. e., extends to more classes 
and individuals ; but the species has more comprehension or 
intension, i. e., includes the part expressed by the genus, be- 
sides the specific difference. 

It is manifest that the differentia may be of three- kinds : 
generic, as for instance the difference between man and tree ; 
specific, as that between the different species, horse and cow ; 
and individual, as between Byron and Moore as poets ; but 
each becomes, in reference to the genus above, a specific dif- 
ference. 



PROPERTY AND ACCIDENT. 47 

(18.) Property and Accident. 
Thus, having shown the relations between the genus, or the 
whole essence, the species, and the differentia, parts of the 
essence, each of which is expressed by a common term, we 
come to consider those things which are or may be joined to 
the species or essence. They are divided as follows : 

I. Property, which is joined universally to the essence, and 
thus must be asserted as belonging to every individual of the 
species ; and, 2d. Accident, which is joined only contingently, 
that is, to one individual or certain individuals of the species, 
and not to the whole species. 

Property is of two kinds : 1st. That which is universal, or 
belonging to every individual of the species, but not peculiar 
to the species, as respiration, which, although it belongs to all 
men, is not confined to the species man. 2d. That which is 
universal and peculiar, as the power of intelligent speech, which, 
while man as a species possesses it, is peculiar to man. Some 
writers have erred in enumerating a third kind, viz. : peculiar, 
but not universal, as, for example, to be able to be a poet. But 
this violates our definition, since, if it belong to some indi- 
viduals and not to the species," it ceases to be a property, and 
becomes an accident. 

II. Accident is something joined contingently to the species, 
or belonging only to certain individuals of it. 

Accident is of two kinds, separable and inseparable. A 
separable accident is a circumstance which may be detached 
from the individual without affecting his identity or altering 
our general conception of him ; as John is walking or is lying 
down ; in which examples the accidental circumstance of walk- 
ing or lying down is not a necessary part of the individual, 
but may be detached from him, so that we may still conceive 
of him as doing neither. 

An inseparable accident is one which cannot be detached 
from the individual ; as, born in Philadelphia, born in 1800. 

It is by means of such inseparable accidents that a man is 



48 logic. 

described or his history written ; but it must be remarked that 
this phraseology is rather convenient than exact, for as soon 
as the event which we call a separable accident occurs in the 
life of an individual, it really becomes inseparable. Thus, if 
John ivalked to the city on a certain day, or, being unwell 
afterwards, was lying down in consequence, we can no more 
detach these facts from his history than we can the event of 
his being born in a certain place and at a certain time; but as 
they are unimportant, we make no life-record of them. 

Having now illustrated the meanings of genus, species, 
essence, differentia, property and accident, let us, for conveni- 
ence and clearness of illustration, write out a sentence em- 
bodying all these uses of common terms, as a model by which 
the student will easily frame other examples for himself. 
This sentence will also embody the different processes of 
generalization. 

(property universal 
(individual) (species) (differentia) (genus) but not peculiar) 

John is a Man = a rational animal, who breathes, has the 

(property universal 

and peculiar) (separable accident) (inseparable 

faculty of speech, is lying on the sofa, and was born in Phila- 

accident) 

delphia. 

The logical name given to every common term representing 
a genus, species, differentia, property, accident, is predicable; 
viz., something which may be predicated : no other terms than 
these are predicable. 

(19.) Of the Different Orders of Genera and Species. 

A summum genus, or highest genus, is the highest class of 
all, and has no -genus above it. 

A term which expresses at once a genus and a species is 
called a subaltern genus and species. For example, quadru- 
ped is a genus of horse and a species of animal. 

In the descending scale from the summum genus, the suc- 
cessive or inferior genus is called a subaltern genus. 



DIFFERENT ORDERS OF GENERA AND SPECIES. 49 

In the ascending scale from the lowest species, it is called 
the subaltern species. 

When a genus is divided into its species, they are called 
co-ordinate or cognate species, to indicate that they are not 
subordinate to each other. Thus, if quadruped be divided 
into horse, cow, lion, as representing the equine, feline and 
vaccine races, these would be cognate species. ^ 

A species which contains beneath it no oilier species, but 
only individuals, is called an infima or lowest species. In any 
scientific investigation, however, ranging between any two 
limits, although not absolutely the highest and lowest, it is usual, 
for convenience, to call the highest limit named summum 
genus, and the lowest infima species; as though we should 
say, " Let A be the summum genus and C the infima species 
during this investigation." There are also in common use 
the phrases proximum genus and remote genus, the first of 
which means the genus next above, and the second a genus 
farther removed from the species in question. Thus, quadru- 
ped is the proximum and animal the remote genus of horse. 
It is necessary that the proximum genus should be the genus 
next above the species in question ; but the remote genus may 
be any one farther removed, and not necessarily the summum 
genus, which is, of course, the most remote. 

It must be observed that the use of a common term, as 
either species, genus, differentia, property or accident, is a rela- 
tive use ; and because it is used with one of these significa- 
tions in one sentence, this does not deter us from using it 
with quite another meaning on another occasion. Thus if 
we take the word red, we shall find we can make it serve as 
each in turn. 

The color Red is a genus under which as species are ranged 
pink, scarlet, crimson, vermilion, etc., the different kinds of 
Red. 

Red is a species of the genus color, and ranges with white, 
blue, yellow, etc., as cognate species. 
5 D 



50 LOGIC. 

Red is a differentia of the " Red rose" which distinguishes 
it from other roses. Red is a property of blood ; and an 
accident of a house, separable if it be painted red, inseparable 
if it be built of Red stone. And thus in analyzing any sen- 
tence we must be careful to ascertain the real value of the 
common terms employed. 

(20.) Realism and Nominalism. 

While upon the subject of common terms, it is well to refer 
to the long-standing controversy between the Realists and the 
Nominalists, which, although it became strangely intermixed 
with theology and church polity, had its origin in the signifi- 
cance of a common term. It will be referred to more at length 
in the historical view. The Realists contended that every 
common term was the name of something really existing — that 
a genus and a species were real things; while the Nomi- 
nalists believed that we obtained common terms merely to 
express a certain inadequate, undefined notion of one indi- 
vidual, which we apply to many, and that thus species and 
genera are mere names that have in nature no correspond- 
ing reality. 

It would seem to be a trivial subject for controversy, but 
the more we examine it the more difficult and subtle it ap- 
pears. Like many subtle controversies, it seems to be of lit- 
tle consequence in which way it could be decided ; but it had, 
to the disputatious Greeks and the more disputatious School- 
men, a charm on account of its subtlety, which its value 
could not secure to it. 

Not to detain the student, let us state the true nature of 
the question, and solve the difficulty by saying, that genera 
and species are merely universal ideas, and as such exist 
only in the mind ; that they are expressed by common terms, 
but that they have a real foundation in the individuals from 
which they have been acquired. 



DEFINITION OF TEEMS. 51 

(21.) Definition of Terms. 

Definition* is applied to terms in their logical use, and 
means limiting them in such a manner as to distinguish them 
from all and any other terms. 

As much error arises from the indistinctness of terms, and 
the fact that different persons employ them in different mean- 
ings, just definitions which may bind both parties in a con- 
troversy are very important. 

A definition is usually put in the form of a categorical 
proposition, of which the subject is the term to be defined, and 
the predicate is the definition proper. Thus in the example 
"Man is a rational animal," the whole sentence is called the 
definition. This is not, however, strictly speaking, correct ; 
as the predicate alone, " rational animal" defines " man," as 
if in answer to the question " what is the definition of man?" 

The first division of definition is into two kinds, essential 
and accidental. Essential definitions are further divided into 
physical and logical. 

The second division of definition is into nominal and real. 
Before explaining the meaning of these divisions, we shall 
arrange them, for the sake of convenient reference, into a 
tabular statement. 

DEFINITION. 

1st division. (divided into) 2d division. 



Essential. Accidental. Nominal. Real. 

(div. into) 



Physical. Logical. 

An essential definition is one which presents to us the prin- 
cipal parts of the essence of the thing defined; thus, a steam- 
boat is " something consisting of hull, engine, wheel-houses, 
smoke-pipe, etc. ;" or, again, it is " a vessel for water trans- 
portation propelled by steam." In each case the form of our 
* De and finio, more remotely finis. 



52 LOGIC. 

essential definition would be induced by the character of the 
person asking the definition, and according to the information 
he desired, but always in terms of the essential parts of the 
object for which the term stands. But it must be particu- 
larly observed that these principal or essential parts are of 
two kinds widely different from each other : physical parts 
or parts which are actually separable by the hand, and Logical 
parts, or those which are only divisible by the mind. To 
explain, a physical essential definition of a ship would be " an 
object which consists of hull, masts, cordage," etc., being the 
parts into which it may be physically divided; while the 
logical parts which would constitute a logical essential defini- 
tion would be the genus, viz., " ocean vessel •" and differentia, 
viz., " of peculiar build ;" which, as we have seen, when com- 
bined make up the species ship. 

(species) (genus) (differentia) 

A ship- — is an ocean-vessel — of peculiar build. 

A logical essential definition, then, in every case, consists 
of the genus and differentia. Logic is concerned with . logi- 
cal definitions alone, but examines the others to distinguish 
between them and logical definitions. And it is likewise true 
that the physical and logical definitions sometimes coincide, 
but this is of rare occurrence. 

An accidental definition, or description, as it has been tech- 
nically called, consists in presenting the circumstances belong- 
ing to an object, and these are its property or accident ; as these 
are generally more descriptive of an animal or object than 
the material part or part common to all, which is the genus, 
or the differentia which distinguishes the species in question 
only from its co-ordinate species. 

From what has been said before, it will appear that in 
describing a species w T e can only use properties, as accidents 
attach alone to individuals, while properties belong to every 
individual of a whole species ; we should use, besides, proper- 
ties which are universal and pecidiar, since, as they belong to 



NOMINAL AND EEAL DEFINITIONS. 53 

every individual of the species, and to none out of it, we thus 
find its own characteristics ; whereas if we used the proper- 
ties which were universal but not peculiar, we should only 
know characteristics which marked that species in common 
with others, and thus not define it. Thus if we should 
describe man as "a beiug who lived and breathed," this would 
not define or describe him justly. So, too, in describing an 
individual, as for instance in biographical notices, we should 
not use separable accidents which are not a permanent and 
necessary part of the object, but inseparable accidents which 
belong necessarily and permanently to it. For example, if 
we say " William was the Duke of N ormandy who conquered 
England in 1066," we describe him by means of the insepa- 
rable accidents, viz., that he was Duke of Normandy, and 
that he conquered England. 

(22.) Nominal and Real Definitions. 

We come now to the second division of definitions, into 
nominal and real. 

A nominal definition is one which gives the meaning of the 
term which is used as the name of the thing. In brief, it de- 
fines the name. Thus, " a telescope is an instrument for view- 
ing distant bodies." " The photograph is a painting made by 
light on sensitive plates." " The decalogue is the table of the 
ten commandments." 

A real definition analyzes and explains, not the name of 
the thing, but the thing itself; enumerating, besides, all its 
important characteristics and properties; thus, a real defi- 
nition for a telescope would be a treatise on the construction, 
powers, and uses of the instrument, and a real definition of 
the decalogue would be given only by reciting all its command- 
ments. 

In the investigations of science it is evident that the aim 
is to obtain real definitions, and the fuller and more complete 
they are the greater their value ; but since in Logic we have 

5* 



54 LOGIC. 

only to do with the names of things, and not with their subject- 
matter, or the conceptions which they convey to us, it is evi- 
dent that we only need nominal definitions and not real; and 
indeed, with regard to matters of general information, a nomi- 
nal definition will be sufficient to settle the grounds of a con- 
troversy ; for while it is the name that indicates the individual 
or the class, the definition explains the name. 

We may even, sometimes, provided both parties to an argu- 
ment agree to do so, consider as a definition something which 
is purely hypothetical, but which still partakes of the nature 
of a definition ; thus, for example, in an astronomical prob- 
lem we say, "let C be the sun's place in the heavens;" or in 
any case, for purposes of illustration, " let so and so be so and 
so." This form of definition is purely relative ; for although, 
in reality, C is not the sun's place, it is so relatively to the other 
points on the diagram. 

It must also be observed that it is not necessary to the just- 
ness of a definition that it should refer to real things, as, for 
example, we define an unicorn to be " a fabled animal, having 
but one horn," and a phoenix to be "a bird fabled to live with- 
out a mate and to rise from its own ashes." 

(23.) Rules for Definition. 

So important has the subject of definition been considered, 
that Logicians have laid down three rules for it, to which, if 
we adhere, we shall insure just and adequate definitions. 

1st. The definition must give to the mind a clearer concep- 
tion than the name of the thing defined, or it will be useless. 
The clearness of a definition is opposed by negative attributes ; 
thus to define man as not a quadruped would be unsatisfactory 
in this respect. 

In most of the arts and sciences this consists in putting 
a technicality into plain language, for those who are unin- 
itiated ; but if I am asked to define cow, a word understood 
by every one, and say that cow is a ruminant quadruped, I 



RULES FOR DEFINITION. 55 

violate the rule. In the nomenclature of science many tech- 
nical terms give, in one word, what it would require much 
circumlocution to express in common words. Accompanying 
this rule there is the caution that the character of the defini- 
tion should depend upon the subject and the persons addressed. 

2d. The definition must be adequate ; that is, neither in- 
clude other things than those necessary to define, nor exclude 
any necessary explanation of the thing defined. 

Thus, if I define bird to be " an animal that moves in the air 
by means of wings," I am too extensive in my definition ; as 
that would include other animals than birds, as bats, flying 
fish, etc.; and if I define it to be u a feathered animal that 
sings" that would be too narrow, as some birds do not sing. 

3d. The third rule is rather a caution which grows out of 
the other two than a rule like them. It is, that the words 
used in a definition shoidd be sufficient and of the proper kind 
to define the thing. 

If we use too many words, we confuse the meaning and are 
liable to tautology; if too few, we are liable to obscurity. 
Thus, to say that " a square is a four-sided figure with equal 
sides" would be true but not definite, as there may be drawn 
other parallelograms not right angled, with equal sides. If 
we say "a parallelogram is a four-sided figure whose opposite 
sides are equal and parallel" we use too many words, as the 
equality of the sides implies the parallelism, and vice versa. 

In the first case we err, because we do not exclude, in our 
definition of the square, all other figures ; in the second, be- 
cause we allow it to be supposed that there are four-sided 
figures whose opposite sides are equal and not parallel. 
Under the head of tautology comes what is called Defining 
in a Circle ; i. e., by using the term to be defined in the defi- 
nition. Eight is man's power to do or not to do. Law is a 
legal ordinance ; evil is that ivhich is not good. 

The examples taken are broader and more apparent than 
those in which faulty definitions are generally used, but they 



56 LOGIC. 

render the error more obvious, and indicate to us the charac- 
ter of the danger to be avoided. 

If we would see the practical necessity of definitions, we 
need but consider a few of the vague and inexact terms 
which we use in our ordinary speech, and which it seems a 
prevailing fashion to distort in their meanings. We shall 
recur to this subject under the general title of " Verbal Fal- 
lacies," but may now give a few illustrations of the value of 
exact definitions. Take for example such words as Necessity 
and Necessary, which may mean either an accordance with 
the invariable law of God, or an obedience to the blind de- 
cree of fate, according to the belief or skepticism of him who 
uses them. In its political sense, the adjective necessary has 
been said to be capable of certain degrees of comparison, as 
in the argument urged in favor of the Bank of the United 
States,* in speaking of the means necessary for carrying out 
the provisions of the Constitution, it was asserted that they 
may be classed under the three categories of necessary, very 
necessary, and absolutely and indispensably necessary. So also 
in religion, certain things are said to be generally necessary 
to salvation, while others are said to be absolutely necessary. 
Thus the technical sense of the word is entirely lost, as that 
refers to an absolute condition, which cannot but be, or cannot 
be otherwise, and therefore does not admit of comparison. 
Or if we would see a strange, conglomerate example of indef- 
inite and erroneous terms, demanding a clear definition, take 
the war-cry of the French revolutionists, "Liberty, Equality, 
Fraternity ;" no one word of which can express to the people 
a distinct idea, or will bear the test of a clear definition. 

It has been a custom in nominal definitions to define one 
term by means of its synonym, borrowed from another lan- 
guage. Although our language is, in its structure and the great 
majority of its principal words, Anglo-Saxon, still the large 
number of French and Latin words which have been brought 
into it have formed terms synonymous with the original Saxon ; 
* Kent's Commentaries, vol. i., Lect. 12. 



RULES FOR DEFINITION. 57 

but, when they had become naturalized, as we had no use for 
two words exactly synonymous, wisdom suggested that they 
should exhibit shades of difference in meaning, which did not 
originally belong to them ; so that few if any words are justly 
defined by their synonyms. Besides, as a similar idea among 
any two people would have its differences drawn from their 
own peculiarities of clime, and race, and manner of life and 
government, the synonyms when brought into the language 
would often express great differences at once, and without 
•any effort on our part to cause them to do so. As a remark- 
able instance of this, let us see how very wrong it would be 
to define our English word freedom by its synonym liberty, 
which comes to us from the Latin ; and yet, how many con- 
found the two. Indeed these are historic Avords, and give us 
an insight into the times of their birth, wonderfully illus- 
trative of the people and countries from which they came. 
Freedom is the personal, individual independence and right 
of every man, his free doom; i. <?., free province or jurisdic- 
tion from his birth. Coming as it does from the Teutonic 
element in our language, it tells us of the free and independ- 
ent Germans, who, by their own valor, overturned the great 
fabric of the Roman empire. They were men of the forest 
and mountain, inhabiting no cities — there were none in Ger- 
many till after the eighth century — but only roving where were 
the lordliest spoils, and claiming them as the reward of their 
personal freedom. On the other hand, liberty tells us of the 
Roman cities, of the sway of the Roman empire, and of 
Roman licentiousness ; of a form of manumission, implying 
slavery; individuality merged into citizenship. To be a 
Roman citizen was to have attained the post of honor, open 
to all advancement in diplomacy and war. Nor is the spirit 
belonging to these words yet lost. While we cling like good 
citizens to our liberty, vouchsafed to us by the constitution of 
the country as Americans, we much more desire to keep well 
guarded that freedom of opinion, of speech, of action^ which 
is our indefeasible right as men. 



58 LOGIC. 

In view of the importance of just definitions, let us under- 
take do controversy or expression of opinion involving a 
vague and indistinct term, without demanding a definition, 
and agreeing to use it during the discussion. 

(24.) Division. 

It is of great importance in the consideration of common 
terms which stand for classes, that we should be able to divide 
them into all their several parts or significates. An individ- 
ual, as its name indicates,* is incapable of logical division. 
It is only a species or genus — i. e., a class, in more general 
language — which can be so divided/ 

Division is of two kinds, physical and logical; to these 
some writers add, improperly, numerical division. 

Physical division, also called partition, is the actual separa- 
tion of the physical parts of which a thing is composed. It 
is evident that an individual is capable of physical division; 
thus, an individual tree, as a certain oak, may be divided into 
trunk, branches, and these further subdivided into hark, heart, 
leaves, etc. ; an individual man, as John, may be physically 
divided into head, arms, trunk, legs, etc. With this kind of 
division Logic has directly nothing to do. 

Logical division, which takes place in the mind only and is 
only ajoplied to classes, consists in separating a genus into its 
different species ; and a species into the individuals composing 
it ; and this in regular order from the summum genus to the 
infima species. Thus, the genus tree would be logically divi- 
ded into oak, maple, hemlock, fir, pine, elm, etc. ; and the species 
oak, into red oak, white oak, live oak, scrub oak, etc. ; and each 
of these again into the individual trees comprising its kind. 

It will be evident that in a just division, each one of the 
parts — denoting a species — will be less than the whole num- 
ber which make up the genus; or any one of the parts — 
denoting an individual — will be less than the whole number 
* In and dividuus, from divido, to divide. 



DIVISION. 59 

which make up the species ; or, as a test of the correctness 
of the division, we must be able to predicate the summum 
genus of any one of the parts. 

If, for example, we have assumed tree to be the summum 
genus, we must be able to predicate tree of oak, or live oak, or 
any individual live oak. 

It is evident that the same term may be logically divided, 
according to race, into Caucasians, Malays, etc. ; according to 
creeds, into Buddhists, Jews, Mohammedans, Christians, etc. ; 
according to nation, into Americans, English, French, etc. 
These cross-divisions must not be mingled or confounded ; 
for example, to divide man into Caucasians, Mohammedans, 
Americans, etc., would be false and useless division. 

The principle of division is best illustrated by a scheme, or 
inverted tree, in which are arranged clearly, symmetrically, and 
without arbitrariness, the different parts of the division. 

SCHEME OF DIVISION.— SUMMUM GENUS. 

TREE. 

Oak. Maple. Pine, etc. 



Live Oak, White Oak, Red Oak, etc. Sugar Maple, Common Maple. 



Individual Trees. Individual Trees. 

It may be well to observe particularly an auxiliary phrase, 
according to, which we use to keep us from a simple but dan- 
gerous error ; i. e., every division should be governed by one 
and a single principle. Man is divided not into races, creeds, 
nations, etc., but according to these, into various parts, thus : 

SUMMUM GENUS.— MANKIND DIVIDED ACCOEDING TO 

Eace. Creed. Nation. 



Caucasian, Malay, etc. Jews, Christians, Mohammedans. English, French, German, etc. 



60 LOGIC. 

It is evident that all the co-ordinate species must be on the 
same line or platform, that is, they must hold the same rela- 
tive position to the summum genus. We must be careful to 
omit no subaltern genus; and we must place each subaltern 
genus in its own relative grade. Thus, if we should place 
oak properly, in the division of tree, but should pass immedi- 
ately from the genus tree to the species sugar maple, thus leav- 
ing out the species maple, co-ordinate to oak, we should make 
an unequal and undue division. This would be placing one 
of the co-ordinate species on the same level with one subordi- 
nate to it. In other words generic, specific and individual 
differences must determine the systematic arrangement. To 
sum up : 

I. The species constituting the genus must exclude one 
another. 

II. All the species taken together must be equal to the 
genus divided. 

III. The division must be made according to one single 
principle. 

From what has been said, it will be seen that the process 
of Division is exactly the opposite of Generalization. 

As in Generalization we disregarded the differences between 
many individuals, or between many species, and considered 
only the properties they had in common, that we might 
constitute them respectively species and genus, calling them 
by a common name, so in Division we take the genus thus 
obtained and add to it the several differences which we had 
removed in Generalization, and which distinguish its parts, 
that we may call the parts thus enumerated by separate 
names. 

The two inverse processes of generalization and division may 
be plainly illustrated by a scheme or double tree ; and this 
may be made as full as we please : thus, from individual trees 
we may generalize to the genus tree; or, from trees and shrubs 
and other kinds of vegetation, we may generalize to the sum- 



DIVISION. 61 

mum genus vegetable. The division will be of the exact spe- 
cies, etc., but in the inverse order. 

SCHEME OF GENEKALIZATION AND DIVISION. 

Individual Trees. Individual Trees. Individual Trees. 



Live Oak, Red Oak, etc. Sugar Maple, Common Maple, etc. "White Pine, Yellow Pine, etc. 



Oak. Maple. Pine. 



Oak. Maple. Pine. 



Live Oak, Red Oak, etc. Sugar Maple, Common Maple, etc. White Pine, Yellow Pine, etc. 



Individual Trees. Individual Trees. Individual Trees. 

What has been called mathematical or numerical division is 
in reality but a form of physical division ; thus, I divide a 
loaf into slices, or an apple into pieces, physically, with or 
without regard to the equality of the pieces, or their sizes 
relatively to each other. If this equality or relation be ob- 
served, it may be called numerical division, but it is only an 
exact form of physical division ; as a half, a third, ten times 
as great, etc., etc. 

By a comparison of the subjects of Division and Definition, 
it will be seen that division is, after all, but a systematic and 
practical kind of definition, since there can be no better way 
to illustrate the meaning of tree than logically to divide it, 
before our eyes, into all its species down to individual trees. 

It will be readily seen that the nature of the logical division 
of terms will depend much upon the science in which they are 
used, and the principle according to which they are to be 
classified. Thus, an ethnologist would divide mankind accord- 
ing to races, a theologian according to creeds, and a statesman 
according to nation. The principle of all the divisions would 



62 LOGIC. 

be the same, while the resulting cross-divisions, as we have 
seen, will be widely different. 

(25.) Recapitulation. 

It will be well to recapitulate briefly what has been said 
upon the subject of terms, and the various operations which 
concern them. We have shown — 

1st. That a term is the expression of an object of appre- 
hension, and have explained the different kinds of terms, 
according to a regular division. 

2d. That common terms are obtained by the processes of 
Abstraction and Generalization. 

3d. The distinction between genera, species and individuals, 
etc. 

4th. The Definition of terms, and just rules for definition, 

5th. Division of terms, with the difference between physical 
and logical division, and special consideration of the latter. 

The next step will be to combine these terms into proposi- 
tions ; that is, from our knowledge of two of them to assert 
their agreement or disagreement. 



CHAPTEE VI. 

(26.) Propositions. 

A proposition* is an act of judgment expressed in language, 
and consists of three parts, a subject, a predicate and a copida ; 
the subject and the predicate are called the terms or extremes 
of the proposition. 

The subject, in the due order, is placed first, and is that of 
which something is predicated, i. e., affirmed or denied. 

The predicate is that which is affirmed or denied of the 
subject. 

The copida is always, in categorical propositions, the uniting 
word which expresses the agreement or disagreement between 
the subject and predicate, and is always some part of the verb 
to be. When the copula is affirmative, agreement is expressed ; 
when negative, disagreement. 

subj. cop. pred. snbj. cop. pred. 

A is B = (Csesar) is (a tyrant). 

subj. cop. pred. % subj. cop. pred. 

A (is not) B = (Csesar) (is not) (a tyrant). 

The negative particle, it must be observed, is always a part 
of the copula. 

What appear, in our ordinary speech, to be simple proposi- 
tions are sometimes inverted or elliptical forms of expression, 
which must be put into simple logical form before they can 
be considered as propositions. 

Thus we say " I hope to see you," " I desire to remain ;" 
and in these cases the subject is really placed last; the true 
meaning being 

* From propono, something proposed or set forth for our acceptance. 

63 



64 LOGIC. 

subj. cop. pred. 

( To see you) is (the thing which I hope, or my hope). 

As an example of another form of inversion, we have that 
which springs from the constant use of the neuter pronoun it. 

Thus, in ordinary language, we say, " It is true that I think 
so." The true logical form may be given thus : 

sul>j. cop. pred. 

(That I think so) is (a true thing). 

Many writers have denied that there is such a thing as a 
negative judgment, and consequently that any negation at- 
taches to the copula ; for they say that the proposition John 
is not happy is equivalent to John is unhappy, which transfers 
the negation from the copula to the predicate ; but this is a 
quibble about words, as there are propositions in which the 
negation cannot be thus destroyed, and such is the case with 
far. the greater number. The positive term is generally 
limited and intelligible, the negative unlimited and indefinite ; 
thus, man is a term which we can grasp, but not man includes 
all the universe beside. 

Of the Copula. — The copula may be always reduced to the 
present tense of the indicative mood of the verb to be, and 
consequently expresses neither past nor future time. Thus, 
" Caesar was the conqueror of Gaul," is equivalent to " Caesar 
is the historic personage who conquered Gaul." " I shall be 
glad to see you," is the same as " I am the person who will 
be glad to see you," etc. ; but as this reduction is in general 
unnecessary, we agree to call those propositions which are 
expressed in time other than the present. Very often the 
copula and predicate are expressed together in one word, as 
" The sun shines ;" here the word shines may be resolved into 
is shining, in which is is the copula, and shining the predicate. 
And sometimes, in other languages, as the Latin or Greek, a 
proposition is conveyed in one single word, as amo, I love or 
i" am loving, tu-xu), I am striking ; but in every case, a prop- 



PROPOSITIONS. 65 

osition may easily be placed in such a form that the subject, 
predicate, and copula are distinctly stated. 

But this definition of a proposition, as a sentence consist- 
ing of a subject, predicate and copula, is evidently a physical 
definition, and is not sufficient for our purpose. The logical 
definition of a proposition is "a sentence which affirms or 
denies ;" here proposition is the species, sentence the genus, and 
which affirms or denies is the differentia, or statement of the 
difference between this kind of sentence and all others. The 
word proposition not having in its etymology this strict mean- 
ing, it is very loosely used . to express almost every kind of 
sentence. We must be careful, in Logic, to limit it to the defi- 
nition just given. Hence, we should say that a categorical 
proposition, in its grammatical sense, implies the indicative 
mood, since absolute affirmation or denial is expressed only 
by that mood. Thus are excluded, the imperative mood or all 
commands, the subjunctive mood or all hypotheses, the infinitive 
mood, which, as its name indicates, is not a finite, uniting 
verb, but only a verbal noun. 

If w 7 e examine these moods a little more in detail we shall 
find, first, that even in the indicative mood, questions, or the 
interrogative form of that mood, are excluded, for the use of 
a question implies that one of the parts of the proposition is 
wanting, and that we depend upon the answer to supply it. 
Thus the first and simplest form of the. question is 

Is A B t = Is man mortal ? 

If the answer be affirmative, then we have a right to the 
copula is, which before was wanting, and may write 

A is B = Man is mortal. 

Another form of the question is "What is A?" or "What 

is B?" the answer to which will supply us with the predicate 

and subject respectively. With regard to the subjunctive 

mood there are, it must be observed, propositions which 

6* E 



66 LOGIC. 

assume that form and which are called hypothetical, and they 
come under the class of compound propositions, as 
If A is B, C is D. 

In almost every case the hypothesis is stated in the indica- 
tive rather than the subjunctive mood ; thus, 

If A is B, C is ~D; rather than in the form : 

If A be B, C will be D. 

Of the infinitive mood it may be observed that there are 
various forms ; thus, to ride is pleasant, may be rendered by 
riding is pleasant; horseback exercise is pleasant; plainly 
showing that with the verbal form there is a substantive value. 

(27.) Propositions Divided into Simple and Compound. 

If, now, we proceed to consider first the substance of propo- 
sitions, we shall find them divided according to their substance 
into simple and compound. 

A simple proposition is one which has but one subject and 
predicate, united by the copula is or is not. Simple proposi- 
tions are also called categorical, that is, there is simply 
affirmed or denied an agreement between the subject and 
predicate. 

A compound proposition is one which has more than one 
subject or more than one predicate, and may be resolved into 
two or more simple propositions; as The Delaware and the 
Schuylkill are rivers in Pennsylvania. Compound proposi- 
tions are further divided according to their substance into 
categorical, modal, conditional, causal and disjunctive. 

A compound categorical proposition, like a simple categori- 
cal, affirms or denies the predicate simply and certainly of 
the subject ; thus, 

Alexander, Cozsar and Napoleon were ambitious of military 
glory. 

A modal proposition is one in which the mode or manner 
of agreement or disagreement between the subject and predi- 
cate is stated, as Cozsar conquered Pompey by unfair means. 



QUANTITY AND QUALITY OF PROPOSITIONS. 67 

A conditional proposition consists of two simple categoric 
cals united by the conjunction if; thus, 
If A is B, C is D. 

It is usual, for convenience, to place the conjunction first ; 
the first categorical — A is B — is then called the antecedent, 
and the other — C is D — the consequent. 

A causal proposition is one in which the reason of the truth 
of a simple proposition is stated ; thus, 

Because A is B, C is D. 
A disjunctive proposition is one in which one of two or 
more simple propositions is asserted to be true ; thus, 
Either A is B, or C is D. 

This is done by the use of the conjunctions either and or. 

Propositions are still further divided according to two of 
Aristotle's categories which will be considered hereafter ; 
i. e., according to their quantity and quality. In simple lan- 
guage, Quantity considers of how much of the subject the 
predicate is affirmed or denied ; as, some or all A is B. 

And Quality regards the kind or manner of that predica- 
tion, *. e., whether it be affirmative or negative ; whether A is 
or is not B. 

(28.) Quantity and Quality of Propositions. 
The quantity of a proposition is determined by the amount 
or portion of its subject which we consider. If we assert 
that the predicate agrees or disagrees with the whole subject, 
that is, all the significates which come under the term, the 
proposition is said to be universal; thus, 

All men are mortal, no men are trees, 
are universal propositions, because the whole of the subject is 
considered. But if we assert the predicate to agree or to dis- 
agree with only a part of the subject, the proposition is called 
particular. 



68 LOGIC. 

Some men are brave, few men are good, many men are not 
prudent, are examples of particular propositions. 

The quality of propositions we shall find also to be of two 
kinds — the quality of the subject-matter and the quality of the 
expression. Propositions are divided, according to the quality 
of the subject-matter, into true and false, and, according to the 
form of expression, into affirmative and negative. 

It is evident that with the quality of the subject-matter 
Logic has directly nothing to do ; for, since the logical form 
of a proposition is A is B, it is taken for granted, as we have 
already seen, that this statement is true, and that from the 
very form it assumes. With the subtleties of statements 
Logic is not concerned. Taking for granted the truth of a 
proposition, it makes use of it properly. . Whatever falsity 
lies in it will pervade the argument, but this will not be the 
fault of Logic. In Logic the quality of the subject-matter is 
accidental and not essential. 

The essential quality of propositions in Logic is, then, the 
quality of the expression ; and this quality is made, as before 
shown, to depend upon the copula. If the copula is affirmative, 
the proposition is called affirmative ; as 

All A is B. 
Some A is B. 

If the copula is negative, the proposition is said to be nega- 
tive; as 

No A is B. 

Some A is not B. 

To mark these divisions according to quantity and quality, and 
to simplify the future operations in which they are used to 
frame arguments, we employ letters as symbols. Since every 
proposition must be universal or particxdar, and at the same 
time affirmative or negative, there are four, and only four, 
classes of simple categorical propositions, which we represent 
by the following symbols : 



QUANTITY AND QUALITY OF PROPOSITIONS. 69 

Universal affirmative ; as All X is Y, by A. 
Universal negative ; as No X is Y, by E. 

Particular affirmative; as Some X is Y, by i". 
Particular negative ; as Some Xis not Y, by 0. 

The sign of a universal proposition is the same as that of a 
distributed term ; i. e., the prefix all or every for the universal 
affirmative, and no for a universal negative. 

And here it must be particularly observed that the universal 
negative is only correctly written when in the form no A is 
B. It might at first sight seem that this is equivalent to all 
A is not B ; but it is not so, although often meant to be so ; 
thus, all soldiers are not cruel has a very different meaning 
from no soldiers are eruel. The first is not, indeed, a universal 
proposition, as it appears to be, but a particular, implying 
that some soldiers are cruel, while some are not. 

The translators of our English Bible have, in a few in- 
stances, made use of this form improperly to express a uni- 
versal. Thus, the Hebrew text of the Psalms expresses with 
regard to the wicked : " All his thoughts are ' there is no 
God ;' " while the translators have it, " God is not in all his 
thoughts." The meaning of the translators in this is evi- 
dently, " God is not in any of his thoughts." 

The sign of a particular proposition is the same as that of 
an undistributed term, i. e., the prefix some, jew, several, many, 
and like words, indicating a part only of a ivhole, for particular 
affirmative propositions ; and the same prefix, with a negative 
copula, for partiadar negative. 

But it constantly happens that a proposition has no prefix, 
and we are then thrown upon our knowledge of the subject- 
matter of the proposition, to determine whether it be universal 
or particular. Such propositions as have no prefix to denote 
their quantity are called indefinite propositions, which Logic 
alone will not enable us to understand. We must then look 
to their meaning, and thus find out what prefix is their due. 
For example, men are artists. 



70 



LOGIC. 



By examining the matter of this, we find that only some 
men are artists, and then, making the proper prefix, we declare 
the proposition to be particular. 

Birds fly. This is trne of birds universally, and we have 
the right to prefix the sign all, which denotes it a universal 
proposition. 

A Singular proposition is one which has for its subject a 
singular term ; as 

Alexander was a conqueror. 
Csesar was ambitious. 

It would seem, at a first consideration of the quantity of 
these propositions, that they were particular, but this is erro- 
neous ; they are* evidently universal ; since when I assert that 
Alexander was a conqueror, I mean the whole of Alexander, or 
Alexander taken in his fullest extension. 

As a general rule,' then, singular propositions are universal. 
There are many other divisions of propositions which are 
curious rather than useful distinctions. The above are all 
those necessary to a comprehension of the logical processes 
which follow. 

(29.) Of the Distribution of Terms in Propositions. 

Having treated of the quantity and quality of propositions, 
and observing that, as we have already seen, these proposi- 
tions are to be hereafter used in the framing of syllogisms, we 
come to consider the distribution of terms in propositions, and 
to establish rules for this distribution. If we examine the four 
categorical propositions, with their geometrical notations — 

Affirm A - 1 AU X is Y ' Nee K I No X is Y ' 

Amrm. j 1 S ome X is Y. ^ eg * 0. 1 Some X is not Y. 




first with reference to their subjects, it will be evident that in 



OF THE DISTRIBUTION OF TERMS IN PROPOSITIONS. 71 

A and E the whole of the subject being considered, the sub- 
ject is distributed, as is also indicated by the prefixes All and 
No. It will be equally evident that in J and the subject is 
undistributed, a portion only being taken, as is indicated by 
the prefix Some. 

The rule deduced then, as far as the subjects are concerned, 
is very simple ; it is, that 

All universal propositions distribute the subject. JSfo particu- 
lars distribute the subject. 

But since the predicates in these propositions have no such 
prefixes, how are we to determine whether they are distributed 
or undistributed ? By an examination of the relation exist- 
ing between the subject and predicate in each case, we shall 
see that the distribution of the subject by no means implies 
that of the predicate. 

If we assert, 1st, that All X is Y, we do not assert that 
other things likewise may not be contained in Y ; for though 
All X is Y, All W may be Y; All Z may be Y, etc. ; or, to 
illustrate by a geometrical figure, we have 




showing space enough for other things besides X to be contained 
in Y. Hence, it is evident that the whole of Y is not con- 
sidered in the proposition all X is Y, or that Y, the predicate, 
is not distributed *n a universal affirmative proposition. 

Again, if we take the proposition some X is Y, the same 
reasoning will apply, since many other things may be Y, be- 
sides this some X; as illustrated in the figure 




72 



LOGIC. 



Likewise then we see that the whole of Y is not taken in 
this case, or that the predicate of a particular affirmative 
proposition is not distributed. 

Thus far, then, we have found it true of affirmative propo- 
sitions, whether they be universal or particular, that they do not 
distribute the predicate. 

If, now, we consider the universal negative, no Xis Y, we 
shall find that we must consider the whole of X, and the whole 
of Y, before we can assert that no part of one belongs to any 
part of the other ; thus 




We have already seen that the subject Xis distributed, and 
it thus appears that in a universal negative proposition the pred- 
icate also is distributed. The whole of the subject is brought 
in contact with the whole of the predicate, or we could not 
entirely deny their agreement. It remains now to consider 
only the predicate of a particular negative, some X is not Y. 
The same reasoning applies here as in the last case ; or we 
must know and consider the whole of Y, before we can assert 
that no part of it belongs to the some X in question. 




It therefore appears that the predicate of a particular nega- 
tive proposition is distributed. 

If we collect together these four results, we shall thus 
establish two rules : 



CONVERSION. 73 

1st. The subjects of universal propositions, and not of par- 
ticulars, are distributed. 

2d. The predicate of negative propositions, and not of 
affirmative, are distributed. 

Or, all universals distribute the subject, and all negatives 
the predicate. 

It may be well, for the sake of convenient reference, to 
arrange the quantity and quality of propositions, and the dis- 
tribution of the terms, in a tabular form, so that it may be 
referred to until it be fixed in the mind of the student. 

Four Classes of Categorical 

Propositions. Subject. Predicate. Simple Form. 

A. Universal affirmative. Distributed. Undistributed. All X is Y. 

E. Universal negative. Distributed. Distributed. No X is Y. 

I. Particular affirmative. Undistributed. Undistributed. Some X is Y. 

0. Particular negative. Undistributed. Distributed. Some X is not Y. 

There is a logical process which is passed upon propositions 
and upon propositions only, and this process has in view the 
use which we make of propositions in the framing of argu- 
ments. It is called Conversion. We cannot convert a term, 
nor is it proper to speak technically, as some writers have 
done, of the conversion of arguments. 

(30.) Conversion. 
Conversion consists in transposing the terms of a propo- 
sition in such a manner as to place the subject for the predi- 
cate, and the predicate for the subject. Thus, having the 
proposition A is B, we convert it into B is A. When no other 
change than this is made, the conversion is called simple con- 
version; but by an examination of the four forms of cate- 
gorical propositions, it will be evident that they cannot all be 
simply converted, and retain in the converted proposition or 
converse the truth of the original jyroj)ositio?i or exposita. As 
a simple example of this : having the proposition 

All men are mortal, 
we cannot write the converse, 
7 



74 LOGIC. 

All mortals are men. 

No other conversion is allowed in Logic than that which 
is called illative* or that in which we may infer the truth of 
the converse from the truth of the exposita. 

To simplify this, let us convert each of these propositions 
in turn. 

1. (A.) All X is Y = All m,en are mortals. 

It is evident, as we have already seen, that we cannot con- 
vert this proposition simply, for we cannot read 

All Y is X = All mortals are men, 
since Y (or mortals) includes many other races besides men. 

We, therefore, limit the quantity of the proposition from 
universal to particular, so that Y, which was undistributed in 
the original proposition, may remain so in the converse. Ex- 
pressing, then, this non-distribution of Y by the prefix some, 
we shall have as the converse 

Some Y is X = Some mortals are men. 
From the nature of the process, this form of illative conver- 
sion is called conversion by limitation.^ 

From this we see that the converse of a universal affirmative 
is a particular affirmative, or A becomes, when converted, I. 
If we examine the universal negative, 

2. (E.) No X is Y= No men are trees, 

we shall see that as X and Y are taken in their whole exten- 
sion, or are distributed, we may here convert simply, and read 
No Y is X = No trees are men. 
The converse of a universal negative is a universal negative. 
So, likewise, in the particular affirmative, 

3, (I.) Some X is Y ' = Some men are cruel, 
we shall find that neither subject nor predicate is taken in its 

* In and fero (latum). 

f The Latin name employed by logicians, for this kind of conver- 
sion, is conversio per accidens. 



CONVERSION. 75 

full extent or distributed, and that we may, therefore, con- 
vert simply : 

Some Yis X = Some cruel (beings) are men. 

The converse of a particular affirmative remains a particular 
affirmative. There remains only the particular negative to 
be considered. 

4. (0) Some X is not Y= Some quadrupeds are not horses. 

This proposition presents a special difficulty. We cannot 
convert it simply as in the cases of E and I ; for we should 
then have X, which is undistributed in the exposita, distributed 
in the converse; thus we would have the absurdity 

Some Yis not X = Some horses are not quadrupeds. 

Nor can we invert the process of conversion by limitation as 
in the case of A (1), and pass back from particular to uni- 
versal, as 

AlU Yis not X = All horses are not quadrupeds. 

To overcome this difficulty we detach the negative particle 
7iot in the original proposition from the copula, and attach it 
to the predicate ; thus, instead of the usual form some X is 
not Y, we read, 

Some Xis (not Y) = Some quadrupeds are (not horses), 

and then it is evident that for all logical purposes, the propo- 
sition ceases to be or particular negative, and becomes I or 
particular affirmative, since for (not Y) we might place any 
other symbol, as Z, and convert by simple conversion. But 
without this trouble, if we convert, we shall have 

Some (not Y) is X = Some (not horses) are quadrupeds, 
or, in our ordinary language, to complete the sense, 
Some (beings which are) not horses are quadrupeds. 
This is called conversion by contraposition or by negation. 
We arrive by this process at a rule for illative conversion, 



76 LOGIC. 

which is, that No term must be distributed in the converse which 
was undistributed in the exposita. 

By arranging the different kinds of illative conversion in 
tabular form, we shall simplify them for reference. Taking 
the letter p to indicate conversion by limitation or per acci- 
dens ; s, simple conversion ; and h, conversion by negation, we 
shall have the following table : 

ILLATIVE CONVERSION. 

Original Propositions. Methods of Converting. Converted Propositions. 

(A) All X is Y. p. Some Y is X. (I.) 

(E) No X is Y. s. No Y is X. (E.) 

(I) Some X is Y. s. Some Y is X. (I.) 

(O) Some X is not Y. k. Some (not Y) is X. ( I.) 

The above are the regular forms of conversion, but there are 
certain Additional conversions to be noticed. It must be 
remarked that the universal affirmative, 

All X is Y— All men are mortals, 

is sometimes converted in another manner ; i. e., by putting 
immediately before both subject and predicate the negative 
particle not, and then converting ; thus, 

All (not) Y is (not) X = All (not) mortals are (not) men ; 

i. e., All (who are not) mortals are not men; or, in common 
phrase, None hit Y can be X = none but mortals can be men. 
Again (E), which is converted simply, may be likewise 
converted by limitation, since, if having the universal form, 

No A is B — No men are trees, 
we can say 

No B is A = No trees are men, 

we can also say, what is less than this, 

Some B is not A = Some trees are not men. 

It may happen that for some purpose of logical technical- 
ity it will be better to use the particular when we have a 
right to use the universal, but from the existence of the 



CONVERSION. 77 

universal we infer that of the particular, which is only a 
part of it. 

There remains only one remark to be made upon the subject 
of conversion • it is that there are a few propositions which 
bear the form of A or universal affirmative, which are capable 
of simple conversion. The terms of such a proposition are 
said to be convertible terms, or the predicate and subject are 
either exactly equivalent or exactly co-extensive ; for example, 
in the proposition All common salt is chloride of sodium, we 
have a right to assert that all chloride of sodium is common 
salt. From the proposition All the good are saved, we have a 
right to infer that All {who are) saved are good. Many just 
definitions come under this class. Besides such propositions 
as these, there are many mathematical propositions which 
seem to be single propositions with convertible terms, when 
in reality they contain two distinct propositions, each of 
which requires distinct proof. Thus, All equilateral triangles 
are equi-angular. The apparent converse that All equi-angu- 
lar trianguldrs are equilateral, is indeed true, but this is not 
inferred from the original proposition ; it is proved separately 
by geometricians ; so that, instead of being the converse of 
the proposition stated, it is; in reality, a distinct proposition. 

The processes of conversion have been applied above only 
to the forms of simple categorical proj)Ositions ; they may like- 
wise be applied, however, to compound propositions, and, when 
we come to consider these, we shall show how they may be 
converted ; but it may be here observed, that as all compound 
propositions may be readily reduced to the simple categorical 
form, having shown how to convert these, we have in reality 
shown how to convert them all. 

The next process of importance in considering propositions 
is the manner and character of their opposition to each other, 
and this, like the process of conversion, becomes of special 
value when we are joining propositions together to frame 
arguments. 
7* 



78 LOGIC. 

(31.) Of Opposition. 

Two propositions are said to be opposed to each other 
when, having the same subject and predicate, the one denies 
either entirely or in part what the other affirms, or affirms either 
entirely or in part what the other denies ; as, for instance, the 
proposition 

(A) All men are mortal is opposed by both {^^ZrTnfmortal, (0.) 
and (E) No angels are men is opposed by both {^elng^arlmen. &] 

Again, two propositions are said to be opposed when, hav- 
ing the same subject and predicate, the one affirms in whole what 
the other affirms in part, or denies in whole what the other denies 
in part; thus, 

(A) All men are mortal. ( Opp.) Some men are mortal. ( I.) 

(E) No men are trees. ( Opp.) Some men are not trees. (O.) 
Or, the rule may be more concisely stated thus : two propo- 
sitions are said to be opposed to each other when, having 
the same subject and predicate, they agree in quantity or in 
quality, or in both. 

It will appear, then, that the opposition in propositions is 
both in quantity and in quality, and as there are four forms 
of categorical propositions, and any two may be thus op- 
posed, we shall have four kinds of opposition, which will best 
be illustrated by the following figure : 

Ant contraries p n E 

if s,. TI 

CF % J? FC 



V a 



o 



N t sub-contraries r n 

IF TI 

C T T C 



In which the two universal propositions A and E are called 
contraries and differ only in quality, being respectively affirm- 



OF THE MATTER OF PROPOSITIONS. 79 

ative and negative; the two particulars I and O are called 
sub-contraries, differing likewise in quality only; the two 
affirmatives and the two negatives are called respectively sub- 
alterns, differing in quantity only; the universal affirmative 
and particular negative, and the universal negative and par- 
ticular affirmative, are respectively called contradictories, and 
differ both in quantity and quality. 

If we desire, as in applying Logic we may do, to determine 
the relative truth and falsity of these respective propositions, 
we must look for a moment at the matter which they may 
contain. 

(32.) Of the Matter of Propositions. 

The matter of a proposition is the nature of the connection 
between the terms of the proposition, or, in ordinary language, 
the exact meaning of the proposition. 

By considering the nature of this connection between the 
terms, we shall see that it can be of only three kinds : neces- 
sary, which is expressed by an affirmative proposition ; im- 
possible, expressed by a negative proposition, and contingent, 
which is expressed by a particular proposition. 

To illustrate : if we have given to us the two terms, men 

and mortal, and are told to connect them by a copula, we ask 

ourselves, what is the nature of the connection between these 

two ? The answer is, it is necessary, and we express that 

necessity by using an affirmative copula, and prefixing the 

sign All: 

All men are mortal. 

Again, if we have given to us the two terms men and trees, 
to perform an analogous operation, we shall assert the nature 
of the connection between them to be impossible, and express 
that impossibility by the use of the prefix No — 

No men are trees. 
If, again, we have the terms men and handsome, we assert the 
nature of the connection to be contingent, as some men are 



80 LOGIC. 

and some are not handsome ; and thus to express contingent 
matter we write the proposition with the prefix some : 

Some men are handsome. 
Some men are not handsome. 

If, now, we examine the matter of these propositions we shall 
see that, 

In necessary matter, all affirmatives are true and negatives 

false. . - 

Necessary Matter. 
True. False. 

(A) All men are mortal. (E) No men are mortal. 

(I) Some men are mortal. (O) Some men are not mortal. 

In impossible matter all negatives are true and affirmatives 

false. 

Impossible Matter. 
True. False. 

(E) No men are trees. (A) All men are trees. 

(0) Some men are not trees. (I) Some men are trees. 

In contingent matter all particulars are true and universale 
false. 

Contingent Matter. 
True. False. 

(1) Some men are handsome. (A) All men are handsome. 

(0) Some men are not handsome. (E) No men are handsome. 

From this examination we perceive that if one contrary is 
true the other must be false, but if one is false the other may be 
false also ; if one sub-contrary is false the other must be true, 
but if one is true the other may be true also. But in the case 
of contradictories, if one is either true or false, the other must 
be just the opposite, i. e., false or true. 

It remains to consider the subalterns, which differ in quan- 
tity. If the universal (A or E) be true, the particular (I or 
O) will be true also ; as 

(A) All men are mortal, (E) No men are trees, 

implies implies 

(1) Some men are mortal. (O) Some men are not trees. 



OF COMPOUND PROPOSITIONS. 81 

If the particular I or O be true, the universal A or E is 
not necessarily true. 

(I) /Some islands are fertile does not permit us to infer (A) 
All islands are fertile. 

(O) Some islands are not fertile does not permit us to imply 
(E) No islands are fertile. 

But if the particular be false, the universal must of necessity 
be false also. Thus, the false particular Some men are trees 
would give us also All men are trees as a false universal. 

By summing up these inferences we may state the following 
rules, which must be kept in the memory as we approach the 
subject of Reduction. 

I. Contraries may both be false, but never both be true. 

II. Sub-contraries may both be true, but never both false. 

III. Of Contradictories, if one be false the other must be 
true, and vice versa. 

IV. In Subalterns we reason from the affirmation only of the 
universal to the affirmation of the particular ; but from the 
denial of the particular to the denial of the universal. 

The letters N I C at the corners of the figure indicate 
necessary, impossible and contingent matter ; T means true, and 
F false. 

The passage from one proposition to another in conversion 
and opposition is called by some writers immediate inference. 

With the remark that opposition may be also illustrated 
in compound propositions, or those not directly in the simple 
categorical form, or that such propositions may be reduced to 
this simple form by an easy process still to be explained, we 
pass to the subject of compound propositions. 

(33.) Of Compound Propositions. 
A compound proposition consists of two or more simple 
propositions, united together either by a simple copulate, 
expressed or understood, or by a conjunction denoting an 
hypothesis. 

F 



82 LOGIC. 

Compound propositions are consequently divided into two 
classes, categorical and hypothetical. 

Compound categorical propositions are of two kinds, copulative 
and discretive. 

A copulative proposition consists of two or more subjects 
united with the same predicate, or with two or more predi- 
cates, by the use of the copulative conjunction ; as, 

Men, horses and birds are animals. 

A discretive proposition consists of two simple propositions, 

which are contrasted on account of an apparent inconsistency ; 

as, 

Fox, though dissolute, was a patriot. 

In this a third proposition is implied, viz., the general in- 
congruity of patriotism with dissoluteness. 

Many compound propositions are tacit or implied, and thus 
have the form of simple propositions. 

A hypothetical proposition consists of two or more simple 
propositions united by a conjunction which expresses hypoth- 
esis. This conjunction is usually placed at the beginning of 
the proposition. 

Hypothetical are divided into conditional, disjunctive and 
causal, and take these names from the conjunctions which 
express the condition of the hypothesis. 

A conditional proposition expresses the condition by the 
conjunction if; as, 

If A is B, C is D = If John return, Harry will go. 

A disjunctive proposition is formed with the conjunctions 
either and or; as, 

Either A is B, or C is D = Either the day will be fine or cloudy. 

A causal proposition unites its parts by the conjunction 
because; as, 

A is B because C is D. 
John is well because he is prudent. 



OF COMPOUND PROPOSITIONS. 83 

It is evident, in the case of categorical propositions, that 
they may be at once resolved into the simple propositions of 
which they are composed : thus we may divide the copulative 
pro23osition given into three distinct propositions, viz., 

Men are animals, 

Horses are animals, 

Birds are animals. 

and the discretive may be divided into two, thus : 
Fox was dissolute, 
Fox was a patriot. 

Unlike the compound categorical propositions, the hypo- 

tlieficals contain within themselves the germ of an argument, 

and only require that the hypothesis shall be established, or fail 

of establishment, to arrive at a conclusion. Thus, having the 

proposition, 

If A is B, C is D, 

we need only know whether A is B, in order to state the 

argument and arrive at the conclusion that C is D. 

Conditional propositions, however, may be, in every case, 

reduced to a categorical form, by regarding them as universal 

affirmative categorical propositions, of which the antecedent is 

the subject, and the consequent the predicate. We then rid 

ourselves of the condition, by the use of the words " the case 

of;" thus, instead of the form, If A is B, C is D, we shall 

have 

(The case of) A being B, is (the case of) C being D, 

which is purely categorical in form. 

Disjunctive propositions may be reduced to conditionals; 

thus: 

Either A is B, or C is D, is equivalent to if A is not B, C is D, 

or we may place it at once in a categorical form without this 
double process, by reading it thus : 

The two possible cases in this matter are that A is B, and that C is D. 

It is more usual to reduce the disjunctive, however, to a 
conditional form, into which it very naturally falls. 



84 logic. 

The causal proposition, 

Because A is B, C is D, 

becomes either at once categorical, when we establish the 
truth of because, and thus we have 

A is B, therefore C is D, 
as an enthymeme, to which, having the subject-matter, we 
might supply the wanting premiss ; or the causal proposition 
becomes simply conditional, if the cause — expressed by the 
first proposition A is B — be doubtful, and then we read, 
If A is B, CisD, 

which must be treated like the conditional above. 

As it seems, then, that all these are reducible to the con- 
ditional form, we need only show how the process of conver- 
sion is applied to conditionals, in order virtually to apply it to 
them all. From what has been said, it will appear that con- 
ditionals are converted by negation only ; thus, to convert the 
proposition, 

If John has the smallpox he is sick, 
we may read — 

If John is not sick he has not the smallpox ; 

or, the conversion rests upon the fact that the denial of the 
consequent leads to the denial of the antecedent. 

We cannot convert without this negation, for we could not 
reason from the affirmation of the consequent to the affirmation 
of the antecedent; thus, 

If John is sick he has the smallpox, 

since that consequent (sickness) may have sprung from some 
other antecedent than the smallpiox. 

(34.) The New Analytic. 
And here it becomes necessary, before closing the subject 
of propositions, to refer briefly to the effort of certain late 
writers to quantify the predicate; that is, to place prefixes 



THE NEW ANALYTIC. 85 

before it similar to those placed before the subjects of propo- 
sitions to determine at a glance its distribution or non-distri- 
bution, and to form thus a new set or class of categorical 
propositions. Thus, instead of the form all men' are animals, 
they would write all men are some animals, and claim thereby 
not only a greater precision in the logical statement, but in 
some instances the establishment of a distinct proposition ; as, 
for example, 

All A is (all) B. 

It may be admitted that sometimes a new idea is suggested 
by such a quantification of the predicate, but it is only sug- 
gested, not contained in the proposition thus rendered. Thus, 
if we say, 

All men are sinners, 

we mean by our rule, some sinners ; now the question as to 
the comprehension of this word sinners may arise, when we 
place such a prefix ; whether angels and devils may or may 
not be included in it ; and whether the ill-conduct of brutes 
is excluded from it. Whereas, if we could write, 
All men are (all) sinners, 

we should exclude at once all other beings from the category. 
Hence, the quantification of the predicate, which in the old 
system is implied, does, when expressed, suggest new thoughts 
or judgments, but those new judgments rest upon their own 
basis, and have really nothing to do with the original propo- 
sition. There seems really, therefore, nothing gained in the 
extension of the proposition by this attempt to quantify the 
predicate, but rather a confusion of judgment and a compli- 
cation of logical forms. 

It is not intended to give, in detail, the applications of the 
"new analytic," nor to deny that results, totally out of the 
province of .Logic, are attained by it. It is evident that if 
we quantify the predicate, in categorical propositions, we shall 
have four additional forms, viz. : 
8 



86 LOGIC. 





Established Forms. 


New Forms. 




A. 


All A is B. 


All A is all B. 


X. 


E. 


No A is B. 


No A is some B. 


Y. 


I. 


Some A is B. 


Some A is all B. 


U. 


0. 


Some A is not B. 


Some A is not some B. 


Z. 



Now of these new forms we have already considered X, as in 

the case, 

All equilateral triangles are (all) equi-angular, 

and in the cases of exact definitions, as 

All common salt is (all) chloride of sodium. 
In the first we have seen that there are two distinct proposi- 
tions, and in the second that there are but two names for the 
same object. 

As for Y, U and Z, they are so clearly contained in the 
old forms that they need but little elucidation. 

U. Some trees are all oaks, 
when converted gives us 

All oaks are trees, or A. 

Y. No heroes are some men. 

Conv. Some men are not heroes. O. 

Z. Some quadrupeds are not some horses. 

By which we determine that the quadrupeds referred to may 
belong to other species, or may be included in the species 
horse, apart from the some horses mentioned. 




It was attempted, in the new analytic, to simplify the subject 
of conversion, but, it seems, with inadequate results. 

And here we leave the subject of quantifying the predicate, 
so far as it relates to propositions alone. If carried out in the 
syllogism, it would much enlarge the domain of Figure, and 
give much fruitless labor to the logician. 



CHAPTEK VII, 

(35.) Of Arguments. 

An argument is an act of reasoning or ratiocination. It 
consists of two parts : that to be proven, and that by which 
it is proven. 

The part to be proven is embodied in the conclusion, and 
that by which it is proven is embodied in the premisses. 
When these are inverted from the usual logical order, so that 
the conclusion is stated first, it is called the question; and the 
premisses which are joined to it by the word because, are then 
called the reason ; thus, 

(Question) Why are all Americans mortal f 
or All Americans are mortal, 
Because They are men. 

But in logical form and order the premisses are stated first, 
and the conclusion is connected with them by the illative 
conjunction therefore; thus, 

_, . f All men are mortal, 

Premisses i . „ . 

I All Americans are men. 

Therefore All Americans are mortal. 
These two forms must be distinguished from what is expressed 
by the -words inference and proof, which have not to do with 
the order of the parts in an argument, but with the special 
design of the person who uses the argument ; i. e., whether 
from known facts or premisses, he seeks to establish a conclu- 
sion ; or has adopted a conclusion, and is simply seeking for 
premisses by which to substantiate it. 

Logic teaches us to draw from known proofs only a just 
inference, or to maintain a given inference only by just proofs. 

87 



88 LOGIC. 

We may more clearly illustrate by observing how, in the 
various professions, these different methods are used ; thus, a 
naturalist gets together many observations and makes many 
experiments, forming a strong store of proofs, before he may 
justly infer a conclusion, while an advocate at law assumes 
the innocence of his client or the guilt of the prisoner, as a 
foregone conclusion, and then uses every means for obtaining 
proofs and thus establishing premisses by which to substantiate 
his conclusion. 

It has been observed that the logical form of an argument 
is a syllogism, which consists of three propositions ; i. e., two 
premisses and a conclusion. 

After fully explaining the syllogism, we shall consider all 
forms of irregular and abridged arguments, and show, as has 
been asserted, that they may all be reduced to this simple 
form, so that the logical tests may be at once applied to them. 

(36.) Of the Syllogism. 
In the analysis of Logic, the dictum of Aristotle was dis- 
tinctly laid down and illustrated. Its form was : 
No. 1. No. 2. 

All A is B. No A is B. 

All or some C is A. All or some C is A. 

All or some C is B. No C is B, or some C is not B. 

The principle of the dictum is, that ivhatever (B) we pred- 
icate (in the major premiss) of the whole class (All A) ; under 
which class we assert (in the minor premiss) certain individ- 
uals (All or some C) to be ranged ; we may also predicate 
(in the conclusion) of those individuals. 

Thus, B is predicated of (All A), C is an individual of 
the class A, therefore we have a right to predicate B of C. 

But, as few arguments, in the ordinary uses of language, 
are placed in this exact form (although all valid arguments 
may be), there have been laid down two logical axioms and 
several important rules for determining the validity of syllo- 
gisms, without the labor of bringing them to this form. 





mid. 


maj. 




Maj. prem. 


A 


is B 


= 




min. 


mid. 




Min. prem. 


c 


is A 


= 




min. 


maj. 




Concl. 


c 


is B 


= 



LOGICAL AXIOMS. 89 

It must be constantly remembered that it is a condition of 
every syllogism that it contains three and only three terms: 
the major term, the minor term, and the middle term. The 
first two of these terms must not be confounded with the 
jiremisses which bear the same name, and which are proposi- 
tions. Thus in the example : 

mid. maj. 

All men are mortal. 

minor. mid. 

All Americans are men. 

minor. major. 

All Americans are mortal. 

B is the major term, and it is in the major premiss ; C is the 
minor term, and it is found in the minor premiss ; A is the 
middle term, because it is the medium of comparison between 
the other two. In the major premiss, the middle term is com- 
pared with the major ; in the minor premiss it is compared 
with the minor, and in the conclusion, the minor and major 
terms, having been thus found to agree with the same middle 
term, are asserted to agree with each other. 

The minor term is always the subject of the conclusion, and 
the major term the predicate. 

This simple process of comparison leads us to the statement 
of those axioms which determine the conditions of agree- 
ment and disagreement between the major and minor terms, 
and to note some important consequences following from them. 

(37.) Logical Axioms. 
1st. If two terms agree with one and the same third term, 
they will agree with each other. 

2d. If of two terms, the one agree and the other disagree 
with one and the same third term, they will disagree with 
each other. 

Rules. 
I. From the first of these axioms we observe that if both 
premisses ©f a syllogism are affirmative, thus expressing the 



90 LOGIC. 

agreement of the major and minor terms with the middle, the 
conclusion must likewise be affirmative, or express the agree- 
ment between these two terms; thus, B being the major term, 
C the minor, and A the middle, we have 

A is (or agrees with) B, 
C is (or agrees with) A, 

and we must consequently state the conclusion 

C is (or agrees with) B. 

II. Again, from the second axiom, we see that if one of 
the premisses (as the major) be affirmative, and thus express 
the agreement between the major term and the middle, and 
the other be negative and thus express a disagreement between 
the minor term and the middle, we must have a negative con- 
clusion to express the disagreement between the major and 
the minor, which we have thus shown, the one to agree and 
the other to disagree in the premisses with one and the same 
third {the middle). 

Thus, if A is not {or disagrees with) B, 
And if C is {or agrees with) A, 
we must have, C is not {or disagrees with) B. 

III. It is further evident that if both premisses be negative, 
we can draw no conclusion; because in these premisses the 
middle term, simply disagreeing with both the major and 
minor terms, is no longer a medium of comparison between 
them. For example, state the premisses, 

No A is B = No men are trees, 
No C is A = No horses are men ; — 

we have established no relation whatever between C and B, 
or between horses and trees, so that, although we might truth- 
fully write 

No horses are trees, 

it would be an accidental statement, and not spring from the 
premisses stated. 

In the conclusion is stated the relation between the major 



LOGICAL AXIOMS. 91 

and minor term, which was established in the premisses by 
the medium of the middle term. The minor term is the true 
subject of the conclusion, and the major term the true predi- 
cate. Sometimes in an inverted or elliptical conclusion these 
terms may appear transposed, but when properly written out 
they will take the places indicated. 

The middle term, which occurs twice in the premisses, is 
the medium of comparison between the two other terms, and 
is generally the name of a class, of which in one premiss some- 
thing is predicated, or to which some quality is attributed, as 

1. Man is a rational animal, 

in which man is the name of a class, and rationality a predi- 
cate or attribute : under which in the other premiss we range 
an individual or individuals belonging to the class, as 
2. John is a man, 

and by means of which we have a right to predicate or at- 
tribute this same thing rationality to the individual ; thus, 
3. John is a rational animal. 



IV. A?nbiguous middle. 

It is scarcely necessary to state that the middle term must 
be univocal, i. e., must have the same meaning in both pre- 
misses. If it be ambiguous, or possess one meaning in the 
major premiss and a different one in the minor, we shall vio- 
late the first principle in the construction of a syllogism, and 
have four terms instead of the three, and only three, required. 
Most languages have many such ambiguous words, and the 
English particularly is full of them : thus 

1. A bank is a financial institution. 

2. The margin of a stream is a bank. 

3. The margin of a stream is a financial institution. 

Many such glaring examples will occur at once to the stu- 
dent; but it must be remembered that the sophist who would 
construct his artful fallacies to deceive, does not employ such 



92 LOGIC. 

manifestly ambiguous words, but those whose double mean- 
ings are much more nearly the same. 

Thus, in their philosophic meanings, the words church and 
faith have given rise to sharp controversy and violent partisan- 
ships. As ambiguous terms play a very prominent part in the 
subject of Fallacies, we shall recur to them under that head. 
When the argument is written out in symbols, the ambi- 
guity either disappears entirely, that is, when we represent 
the term in both premisses by the same letter, thus, 

A is B, 

C is J, 

CisB, 

or it becomes at once manifest, when we represent the term 
in the major premiss by one symbol, as A, and that in the 
minor, having a different meaning, by another, as D, thus, 

AisB, 

CisD, 

in which premisses there are four terms, and the error dis- 
tinctly appears. 

V. Undistributed middle. 

The middle term must be distributed ; i. e., taken in its 
whole comprehension, at least in one of the })remisses, for it 
will otherwise occur that we may compare the major term 
with one part of the middle, and the minor with another part, 
and thus it would fail to be a just medium of comparison. 
It might happen, by chance, that these two parts should 
be the same, but 'it would be only by chance ; in the gene- 
ral case they would be different parts, and if we choose to 
regard each part as a distinct term, we should again run into 
the error of having four terms instead of three; thus, 
Some quadrupeds are cows, 
Some quadrupeds are sheep, 
Therefore Some sheep are cows. 
White is a color, 
Black is a color, 
Therefore Black is white. 



LOGICAL AXIOMS. 93 

But if one of the extremes be compared with the whole of 
the middle term, and the other be compared only with a part, 
which part is necessarily contained in the whole, they may 
then be compared with each other. 

VI. Illicit process. 

Again, in order to distribute either the major or minor term 
in the conclusion, it must have been previously distributed in 
the premiss in which it occurs : because, we only have a right 
to compare that part of the term with the other, in the con- 
clusion, which we have already compared with the middle in 
the premiss ; thus, 

All men are animals, 
No dogs are men, 
Therefore No dogs are animals. 

The technical name for this logical fallacy is the illicit pro- 
cess. In the example, the major term, animals, which is not 
distributed in the premiss (as it is the predicate of an affirm- 
ative proposition) is distributed in the conclusion (as the pred- 
icate of a negative proposition); this is called an illicit process 
of the major term ; if it be the minor term thus treated, it is 
called an illicit process of the minor term. 

The following is an example of illicit process of the minor. 

1. All men are rational beings, 

2. All men are animals, 

3. All animals are rational beings. 

In this example the minor term animals, which is undistrib- 
uted in the minor premiss — as the predicate of an affirmative 
proposition — is distributed in the conclusion, being there the 
subject of a universal. 

Let it be remembered that this is called an illicit process 
of the major or minor term, not of the major or minor 
premiss. 

VII. If both premisses in a syllogism be particular propo- 
sitions, we can draw no conclusion ; thus, 



94 LOGIC. 

1. Some men are wise, 

2. Some men are foolish, 

leads us to no conclusion. Nor are we benefited if we make 
one of the premisses particular negative; thus, 

1. Some men are wise, 

2. Some men are not brave, 

we are as before without any medium of comparison. 

The fact is as stated ; the causes are various, and will be 
fully explained in the chapter on Figure. 

It is sufficient, now, for the student to know that the cause 
is in every case either an undistributed middle or an illicit 
process of one of the other terms. 

By the foregoing axioms and rules, we extend the range 
of syllogistic forms, and are able to see the validity or inva- 
lidity of an argument without reducing it to the invariable 
formula of Aristotle's dictum. We proceed now to show how 
many of these forms there may be, and the relation they sus- 
tain to the dictum itself; and this brings us to the subject of 
Figure and Moods. 



CHAPTER VIII. 

OF FIGURE AND MOODS. 

(38.) Figure. 

Figure is the technical name employed to designate the 
classification of syllogisms according to the position of the 
middle term with reference to the two extremes in the premisses. 
Now, it is evident that the middle term can have only four 
variations of position, and hence we say there are four figures. 

1st. The middle term may be the subject of the major 
premiss, and the predicate of the minor, and this designates 
the 1st figure. 

2d. It may be the predicate of both premisses, and thus the 
2d figure is designated. 

3d. In the 3d figure it is the subject of both premisses ; and 

4th. In the 4th figure (which is the reverse of the 1st) it is 
the predicate of the major premiss and the subject of the minor. 

If we designate the major term by P (as it is always the 
predicate of the conclusion), the minor term by S (being the 
subject of the conclusion), and the middle term by M, and 
merely state these various positions of the middle term, with- 
out considering or denoting the quantity or quality of the 
propositions in the syllogism, we shall have the abstract syl- 
logism, 



I. 


II. 


III. 


IV. 


Mis P. 


P is M. 


Mis P. 


P is M. 


S isM. 


S is M. 


MisS. 


Mis S. 


S is P. 


Sis P. 


S is P. 


S is P. 



These are called the four figures ; and to the syllogisms 
which occur in them the axioms and rules already laid down 
directly apply. 



96 LOGIC. 

If now we proceed to examine these figures in order, we 
shall find that the first figure is but the symbolical represen- 
tation of Aristotle's dictum, the simplest form of the syllogism. 
There will be four variations of it, viz. : 



1. 


2. 


3. 


4. 


All M is P. 


All M is P. 


No M is P. 


No M is P. 


All S is M. 


Some S is M. 


All S is M. 


Some S is M. 


All S is P. 


Some S is P. 


No S is P. 


Some S is not P. 



We have simply supplied the quantity and quality required. 

Since, in the major premiss, then, of Aristotle's dictum, we 
assert or deny the predicate of the ivhole class which is the subject 
(All M),.it is evident that in the first figure, the major premiss 
is always universal. If, then, with this relative position of the 
middle term, i. e., in the first figure, we find a syllogism the 
major premiss of which is particular, we may at once declare 
it to be invalid. 

Again, since the province of the minor premiss in the dictum 
is always to assert that certain individuals belong to the given 
class (and in no case to deny it), it appears that in the first 
figure the minor premiss must always be affirmative, so that 
if we find a syllogism in this figure with a negative minor 
premiss, we may at once declare it invalid. 

Thus, in stating the four forms of the dictum, we have 
stated the only four forms which the first figure can cover. 

But the other figures, which are not directly in the form 
which the dictum assumes, instead of being explained by it, 
are to be considered in the light of the axioms and rules for 
determining the validity of syllogisms when the dictum does 
not directly apply. By examining the second figure, 

P is M, 
S is M, 
S isP, 

we shall find that there are several forms which it will assume 
when we supply the quantity and quality to the propositions. 



FIGURE. 97 

We observe at once that the conclusion must in every case be 
negative, because — 

1st. The middle term is the predicate of both premisses. 

2d. The middle term must be distributed at least once in the 
syllogism. 

3d. In order that the predicate of a proposition shall be 
distributed, the proposition must be negative. 

4th. This will give us one negative premiss, and by the 
second axiom, if we have a negative premiss, the conclusion 
must be negative {universal or particular). 

Third Figure. 
M is P, 
M is S, 
S is P. 

By the supplying of quantity and quality, this figure as- 
sumes a greater variety of forms than any other. 

By considering the position of the terms here, it will appear 
that we can only draw particular conclusions. For if both 
premisses be affirmative, and we draw a universal conclusion, 
or All S is P, then S (the minor term), which was undistrib- 
uted in the minor premiss (being the predicate of an affirma- 
tive proposition), will be distributed in the conclusion, as the 
subject of a universal ; or we shall have an illicit process of the 
minor. 

If the major premiss be negative, and we draw a universal 
conclusion, it is easily shown that the same error — an illicit 
process of the minor — obtains ; and if the minor premiss be 
negative, we shall have an illicit process of the major. 

Fourth Figure. 
P is M 3 
M is S, 
S is P.' 

The fourth figure, which was not proposed by Aristotle with 
the other three, and only recently adopted by logicians, is an 
9 G 



98 LOGIC. 

inversion of the first, and an unnatural and unnecessary form 
of the syllogism. By a similar examination of all the terms, 
we shall fiud that we may draw, as conclusions, in this figure 
all the categorical propositions except A, which, as has been 
shown, can only be drawn in the first figure. It is the pre- 
rogative of Aristotle's dictum alone, to draw from certain 
premisses a universal affirmative conclusion. 

The various forms of the syllogism due to the different 
quantity and quality of the propositions composing them are 
arranged, in the different figures, in what are called moods, or 
a concise manner of expressing a syllogism by symbols. 

(39.) Of Mood. 
If, having any syllogisms, as the following — 

All A is B, (A) fNoAisB, (E) 

All C is A, (A) 2. ■] Some C is A, (I) 

All C is B, (A) (. Some C is not B, (O) 

we write together the symbols characterizing each proposition 
which composes them, we are said to determine the mood of 
the syllogism; thus, the symbol of the major premiss in the 
first syllogism is 

A, or universal affirmative ; 
that of the minor, 

A, or universal affirmative ; 

and that of the conclusion likewise 

A, or universal affirmative. 

Hence we say that A A A is the mood of the syllogism. 

In the second syllogism, we shall find by a similar process 
that the mood is E I 0. 

Now, it is evident that the number of moods we can have 
will depend upon, 1st, the number of propositions in the syl- 
logism, viz., three; and 2d, upon the number of categorical 
propositions which we can enumerate, viz., four, A, E, I, O; 



FIGURE. 99 

it becomes then a simple algebraic arrangement of four letters, 
A, E, I, O, in three columns in every possible combination. 
The number of these possible combinations will be sixty-four. 
For each of the propositions A, E, I and O may have a major 
premiss ; and each of these may have each in turn as a minor 
premiss; thus, 

Maj.prem. Maj.prem. Maj.prem. Maj.prem. 
AEIO 

I I I I I ! I I 1 I I I I I I I 

may have as minor premisses, AEIO AEIO AEIO AEIO 

Again, each of these sets (sixteen in all) may have four 
different conclusions, i. e., each of the categoricals as a con- 
clusion. Taking the first set, for example, and supposing the 
operation performed for the rest : 

FIRST SET. 

Maj. vrem. A. 



1 

Min. prem. A 


1 
E 


I 


I 





1 I 1 1 
Concl. AEIO 


III! 

AEIO 


1 1 1 1 
AEIO 


1 1 1 
A E I 


1 




This same process may be performed for E, I and O. 
There will evidently be sixty-four moods, of which, however, it 
is at once evident that very many will violate the axioms and 
rules already laid down, and must be for this reason discarded. 

Thus, all the combinations of affirmative premisses having 
negative conclusions, as A A E, A I O, etc., etc., must be 
thrown aside, because they violate the first axiom. 

All the sets of negative premisses, with whatever conclu- 
sions, are useless, as E E, O O, E O, O E, etc. 

All the sets of particular premisses, with whatever conclu- 
sions, must be neglected, such as I I, O O, O I, I O, etc. 

If all these eliminations be performed — and, simple as they 
are, the student is advised to go carefully through them once 
for himself — we shall find twenty-eight moods excluded on ac- 



100 LOGIC. 

count of negative and particular premisses : eighteen by the 
condition that the conclusion follows the inferior part, and we 
shall see that one — I E O — is rejected for an illicit process of 
the major term, in every figure, aud finally that of the sixty- 
four arrangements which we call moods, only eleven represent 
■valid arguments, or 



FOUR AFFIRMATIVES 


AND SEVEN NEGATIVES. 


AAA 


E 


A 


E 


All 


A 


E 


E 


A A I 


E 


A 





I A I 


A 













A 







E 


I 







A 


E 









If now we apply these moods to each figure, in detail, it 
would seem, since there are four figures, that we should have 
4 X 11 = 44 moods in all the figures ; but in this application 
we find that many moods which are valid in one figure are 
not in others ; as, for example, the mood I A I, which is 
allowable in the third figure, would be in the first figure a 
case of undistributed middle, and would further violate the 
principle of Aristotle's dictum, which requires that the major 
premiss should be a universal proposition. A E E is a valid 
mood in the second figure, while, in the first, it would have an 
illicit process of the major term, and would further violate 
that principle of the dictum which requires the minor premiss 
to be always affirmative. 

By applying these eleven moods to the four figures, we find 
that there would be six in each figure, or twenty-four in all; 
but even of these, five are omitted as useless ; for example, 
the mood A A I, in the first figure, because it is implied and 
contained in the mood AAA. Since, if the universal con- 
clusion A be true, the particular I is necessarily true. By 
an application of each of these moods to every figure, we 
shall have left, finally, nineteen moods in all ; or, four in the 



FIGURE. 101 

first figure, four in the second, six in the third, and five in 
the fourth. 

The moods of the first figure are called perfect moods ; those 
in the other figures, imperfect moods. 

As it has been asserted that all arguments may be put in 
the form of Aristotle's dictum, that is, that all the imperfect 
moods may be made perfect, we proceed to fulfill this asser- 
tion, by the process of reduction, i. e., the reducing of moods 
in the 2d, 3d, and 4th figures to the 1st figure, which is the 
form of the dictum. 

In order to facilitate this process, as well as to retain easily 
in the memory the different moods and their value, the fol- 
lowing verses, Latin in sound and scansion, but without in- 
trinsic meaning in the words, have been formed : 

Fig. L— B ArbArA, CElArEnt, DArll, FErlO, dato prima. 
Fig. II— CEsAEE, CAmEstrEs, FEstlnO, FAkOrO, secundce. 
ttt _ f Tertia DArAptI, DIsAmls, DAtlsI, FElAptOn, 
[ DOkAmO, FErlsO, habet ; quarta insuper addit. 
Fig. IV.— BrAmAntIP, CAmEnEs, DImArls, FEsApO, FrEsIsOn. 

There are variations in these lines, made by various writers ; 
we have adopted the above as the form which will indicate to 
us in the simplest manner the processes of Reduction. 

Before explaining these lines, which the student must mem- 
orize in order to make them useful, that he may have the 
moods, and their places in the figures, at his tongue's end, it 
will be observed that there are a few words used in these 
verses which are of no use except to make out the hexameter 
lines; of these are dato primoz in the first, secundce in the 
second, tertia habet in the third, and quarta insuper addit, 
which states — moreover the fourth adds, etc. Leaving these 
out of the consideration, in the lines themselves the vowels in 
each word represent the moods; thus, Barbara is the mood 
AAA; Cesar -e, the mood E A E, etc., etc. 

The following consonants indicate what changes are to be 



102 LOGIC. 

made in the given imperfect mood to reduce it to a perfect 
mood of the first figure : — s, that the proposition indicated by 
the vowel immediately preceding it is to be converted simply ; 
thus in Camestres, the first s indicates the simple conversion 
of the first E, or the minor premiss, and the last s the simple 
conversion of the second E, or the conclusion. In similar 
relations p and h stand respectively for conversion by limitation 
and conversion by negation; m, wherever it occurs, expresses 
that the premisses must be transposed ; the other consonants 
have no meaning, and are only employed to frame the words. 
P, in the mood Bramantip of the fourth figure, denotes that 
the transposed premisses, indicated by m, will warrant a uni- 
versal conclusion instead of a particular. The initial letters, 
B, C, D, F, of the words which contain the moods, are so 
arranged throughout the figures as to indicate the mood in 
the first figure to which any imperfect mood will be induced; 
thus Darapti of the third figure will, when reduced, become 
Darii of the first, Camestres will become Celarent, etc. 

It must be observed that this arrangement is only for the 
sake of convenience, as the process of reduction is invariable, 
and the mood Darapti would become, when reduced, the mood 
All of the first figure, whether it were called Darii or by 
some other name. Students are apt to be misled with refer- 
ence to these initial letters, and to suppose that they will aid 
them in the process of reduction. It is on this account that 
they are cautioned that this is only a convenient and not an 
auxiliary arrangement. Before proceeding to explain the 
system of reduction, let us give an example of each mood, in 
all the figures, putting the logical frame-work to its legitimate 
use, and showing every form which the syllogism can assume. 
We shall make the examples very simple, leaving it to the 
student, with these before him, to frame longer and more 
complex ones for himself — a practical exercise which will be 
found very useful. The middle term is placed in italics in 
each example. 



FIGURE. 103 

Examples. 

FIGURE I. 

Barbara. 

A. Every desire to gam by another's loss is covetousness. 
A. All gaming is a desire to gain by another's loss. 
A. All gaming is covetousness. 

Celarent. 

E. No one ivho is enslaved by his appetites is free. 

A. Every sensualist is one who is enslaved by his appetites. 

E. No sensualist is free. 

Darii. 

A. All pure patriots deserve the rewards of their country. 

I. Some warriors are pure patriots. 

I. Some warriors deserve the rewards of their country. 

Ferio. 

E. Nothing which impedes commerce is beneficial to the 
revenue. 

I. Some taxes impede commerce (or are things ivhich impede 
commerce). 

O. Some taxes are not beneficial to the revenue. 

FIGURE II. 

Cesare. 
E. No vicious conduct is praiseworthy. 
A. All truly heroic conduct is praiseworthy. 
E. No truly heroic conduct is (or can be) vicious. 

Camestres. 
A. Every true philosopher accounts virtue a good in itself. 
E. No advocate of pleasure accounts virtue a good in itself. 
E. No advocate of pleasure is a true philosopher. 



104 LOGIC. 

The true middle term here would be {one who) accounts 
virtue a good in itself. 

Festino. 
E. No righteous acts will produce ultimate evil to the actor. 
I. Some kinds of association will produce ultimate evil to 
the actor. 

O. Some kinds of association are not righteous acts. 

Fahoro. 
A. All true patriots are friends to religion. 
O. Some great statesmen are not friends to religion. 

0. Some great statesmen are not true patriots. 

FIGUIIE III. 

Darapti. 
A. All ivits are dreaded. 
A. All wits are admired. 

1. Some admired (persons) are dreaded. 

Disamis. 
I. Some lawful things are inexpedient. 
A. All lawful things are what we have a right to do. 
I. Some things which we have a right to do are inexpe- 
dient. 

Datisi. 
A. All that wisdom dictates is right. 
I. Something that wisdom dictates is amusement. 
I. Some amusement is right. 

Felapton. 
E. No science is capable of perfection. 
A. All science is worthy of culture. 

O. Something worthy of culture is not capable of per- 
fection. 



FIGUKE. 105 

Dokamo. 
O. Some noble characters are not philosophers. 
A. All noble characters are worthy of admiration. 

0. Some (who are) worthy of admiration are not philoso- 
phers. 

Feriso. 
E. No false theories exist in a perfect state of being. 

1. Some false theories are harmless things. 

0. Some harmless things do not exist in a perfect state of 
being. 

FIGURE IV. 

Bramantip. 
A. All oaks are trees. 
A. All trees are vegetables. 

1. Some vegetables are oaks. 

Camenes. 
A. All men are mortal. ■» 

E. No mortal is a stone. 
E. No stone is a man. 

Dimaris. 
I. Some taxes are oppressive. 
A. All (that is) oppressive should be repealed. 
I. Some things which should be repealed are taxes. 

Fesapo. 
E. No immoral acts are proper amusements. 
A. All proper amusements are designed to give pleasure. 
O. Some (things) designed to give pleasure are not im- 
moral acts. 

Fresison. 

E. No acts of injustice are proper means of self-advance- 
ment. 



106 LOGIC. 

I. Some proper means of self-advancement are unsuccessful. 

O. Some unsuccessful (efforts) are not acts of injustice. 

It will be observed that the conclusions in the fourth figure 
are indirectly stated, and that it would seem as if in tracing 
the major term back from its place as predicate of the con- 
clusion, it is in reality predicated by means of the other 
terms of itself; thus, in the conclusion it is predicated of the 
minor, which in the minor premiss is predicated of the mid- 
dle, which in the major premiss is predicated of the major. 
The fourth figure, therefore, is not often used, and is rather 
accidentally stumbled into than employed intentionally. 

• The exact accordancy of the first figure with the dictum 
of Aristotle has been already stated. Of the second figure, 
it may be remarked that it is commonly used to disprove 
something that has been maintained, or is likely to be be- 
lieved, although not true. As an illustration, suppose it had 
been asserted that 

All great statesmen are true patriots. 

Then our example just given of Fakoro would be a refuta- 
tion of this, and the argument would naturally take that 
form. 

Of the third figure, it will appear that it will be useful 
where we have singular terms, which can only be subjects of 
propositions — i. e., never predicates — and also where our pur- 
pose is to offer and sustain an objection to our opponent's 
premiss, which is particular when the argument requires it to 
be universal. 

There are very many inverted and curious forms of argu- 
ments growing out of the elliptical and inverted forms of 
propositions, which we have already considered. Two com- 
mon examples of these are added by way of illustration. 

1. 

None but whites are civilized. 
The Hindoos are not whites. 
The Hindoos are not civilized. 



OF REDUCTION. 107 

The phrase none but whites may be rendered, other than 
whites; and this being the true middle term, we shall have — 

No other than ivhites are civilized. 
All Hindoos are other than whites. 
No Hindoos are civilized. 

Which is evidently a syllogism in Celarent of the first figure. 

2. 
No one is rich who has not enough. 
No miser has enough. 
No miser is rich. 

The major and minor premisses must be put in the form 
of categorical propositions, and we shall have — 

No one who has not enough is rich. 
Every miser is one who has not enough. 
No miser is rich. 

Which is likewise in the mood Celarent. In both these ex- 
amples the minor premiss, which appears to be a negative 
proposition, is in reality affirmative. 

(40.) Of Reduction. 

If we have any imperfect mood — i. e., a mood in the sec- 
ond, third, or fourth figure — and we desire to prove the same 
conclusion in the first figure, so that the dictum of Aristotle 
may immediately be applied to it, the process by which this 
is done is called Reduction. 

Reduction is of two kinds, direct and indirect. Direct 
reduction consists in proving in a perfect mood either the 
same conclusion, or one which, being illatively converted, 
will give us the same conclusion which we had in the imper- 
fect mood. Indirect reduction consists in proving, not that 
the original conclusion is true, but that its contradictory is 
false, from which — by the scheme of opposition — we know 
that the original conclusion must be true. 

Of direct reduction. 

It has been shown that we have a right to convert any of 



U8 LOGIC. 

the propositions of the syllogism illatively; and it is also 
evident that we may transpose the premisses without affecting 
the truth of the propositions or the validity of the argument. 
If, then, we apply the processes indicated by the letters in 
the mnemonic lines, we shall see that they will give us the 
forms of direct reduction. 

Taking for example Cesare, the mood E A E in the sec- 
ond figure ; to write it out we remember in the first place that 
the position of the middle term in the second figure is predi- 
cate of both premisses, and we observe that the major premiss 
is E, universal negative, the minor premiss A, universal 
affirmative, and the conclusion E, universal negative; we 
have then X, being the major, 2i the minor and Y the mid- 
dle term — 

Cesare. Fig. II. 

E. No X is Y = No men are trees. 
A. All Z is Y = All oaks are trees. 
E. No Z is X = No oaks are men. 

The only consonant in the word CEsArE which indicates 
a process of reduction is s, which tells us that the major 
premiss, expressed by the first E, is to be simply converted ; 
performing this operation we shall have — 
Celarent. FiG. I. 
E. No Y is X = No trees are men. 
A. All Z is Y = All oaks are trees. 
E. No Z is X = No oaks are men. 

This syllogism is in the first figure, since the middle term 
Y or trees has become the subject of the major and the pred- 
icate of the minor premiss ; again, 

Fakoro. Fig. II. 
A. All X is Y = All good men are virtuous. 

O. Some Z is not Y = Some warriors are not virtuous. 
O. Some Z is not X = Some warriors are not good men. 

The h expresses that the major premiss (A) is to be converted 
by negation; performing this operation (there is no other 
indicated), we shall have — 



OF REDUCTION. 109 

Ferio. Fig. I. 
E. All (not Y) is not X = All (not virtuous) are not good men. 
I. Some Z is (not Y) = Some warriors are (not virtuous). 
O. Some Z is not X = Some warriors are not good men. 

This process, in effect, changes our middle term from Y or 
virtuous to (not Y) or (not virtuous), while we have the same 
conclusion as before in the mood Ferio of the first figure. 

The reduction of the other moods of the second figure will 

be analogous to those already performed, and the student 

will find no difficulty in reducing them for himself. Passing, 

then, to the third figure, and remembering that in this figure 

the middle term is the subject of both premisses, let us reduce 

the mood 

Disamis. Fig. III. 

I. Some Y is X = Some men are heroes. 

A. All Y is Z = All men are mortal. 

I. Some Z is X = Some mortals are heroes. 

The two letters which indicate changes in the process of 
reducing this mood are s (twice employed) andwi: s indicates 
the simple conversion of the major premiss and the conclu- 
sion, and m the transposition of the premisses ; performing 
these operations, we have 

Darii. Fig. I. 
A. All Y is Z = All men are mortal. 
I. Some X is Y = Some heroes are men. 
I. Some X is Z = Some heroes are mortal. 

Which conclusion is the simple converse of the original con- 
clusion, as was indicated by the final s. 

Fesapo. Fig. TV. 
A. No X is Y = No quadrupeds are men. 

E. All Y is Z = All men are animals. 

O. Some Z is not X = Some animals are not quadrupeds. 

Converting the major premiss simply, and the minor premiss 
by limitation, as indicated by the s and p, we shall have 
10 



110 



LOGIC. 



E. NoXisY 
I. Some Z is Y 
O. Some Z is not X 



Ferio. Fig. I. 
= No men are quadrupeds. 
— Some animals are men. 
= Some animals are not quadrupeds. 



It will be well for the student to reduce every imperfect 
mood, forming for himself particular examples under each. 

Although we have made the subject of Reduction plain by 
the examples already given, we append a table of the man- 
ner of reducing each mood for reference, until the student is 
familiar with them. It is but a recapitulation in tabular form 
of what has been already explained. 



Mood to be reduced. 


Will 
reduce. 




' Cesare. 


Celarent. 


Fig. II. - 


Camestres. 
Festino. 


Celarent. 
Ferio. 




Fakoro. 


Ferio. 




Darapti. 


Darii. 




Disarms. 


Darii. 


Fig. III. ■ 


Datisi. 


Darii. 




Felapton. 


Ferio. 




Dokamo. 


Darii. 




Feriso. 


Ferio. 



Fig. IV. 



Bramantip. 



Camenes. 


Celarent, 


Dimaris. 


Darii. 


Fesapo. 


Ferio. 


Fresison. 


Ferio. 



Barbara. 



Process of Reduction. 



(s) Convert major premiss simply. 

(m) Transpose the premisses, (s&s) 
Convert the minor premiss and 
conclusion simply. 

(s) Convert the major premiss simply. 

(k) Convert the major premiss by ne- 
gation. 

(p) Convert the minor premiss by 
limitation. 

(m) Transpose the premisses, (s & s) 
Convert the major premiss and 
conclusion simply. 

(s) Convert the minor premiss simply. 

(p) Convert the minor premiss by 
limitation. 

(k) Convert the major premis by ne- 
gation, (m) Transpose the pre- 



(s) Convert the minor premiss simply. 

(m) Transpose the premisses, (p) 
Convert the conclusion by lim- 
itation. 

(m) Transpose the premisses. (s) 
Convert the conclusion simply. 

(m) Transpose the premisses. (s) 
Convert the conclusion simply. 

(s) Convert the major premiss simply, 
(p) Convert the minor premiss 
by limitation. 

(s & s) Convert the major and minor 
premisses simply. 



INDIRECT REDUCTION. Ill 

(41.) Indirect Reduction. 

This process, called by the old logicians Reductio ad impos- 
sible, is analogous to the reductio ad absitrdum of geometry. 
It consists in proving that the given conclusion cannot be 
false by proving, in the first figure, that its contradictory is 
false. 

The symbols used to indicate the processes of direct reduc- 
tion do not guide us in the indirect reduction, but we must 
deduce rules for this apart from the other. 

To illustrate, let us take the mood 

Fakoro. Fig. II. 

A. All X is Y = All good men are virtuous. 

O. Some Z is not Y = Some warriors are not virtuous. 

O. Some Z is not X = Some warriors are not good. 

If this conclusion be not true, its contradictory All Z is X = 
All warriors are good, must be true. Assuming this as true, 
and taking it in the place of the minor premiss in the syllo- 
gism, we shall have a new syllogism, as follows : 

A. All X is Y = All good men are virtuous. 
A. All Z is X = All warriors are good men. 

from which premisses by our rules we draw the conclusion 

A. All Z is Y = All warriors are virtuous. 

But this conclusion must be false, because it is the contradic- 
tory of the original minor premiss, and the premisses were 
assumed to be true ; hence one of these last premisses from 
which this conclusion is derived must be false ; but it is not 
the major, for that was one of the originally assumed premis- 
ses ; it must, therefore, be the minor, which we know to be 
the contradictory of our original conclusion ; and the original 
conclusion must therefore be true : this, it will be observed, is 
proven in the first figure, in the mood Barbara. To take 
another example, let us reduce the mood 



112 LOGIC. 

Darapti. Fig. III. 
A. All Y is X = All gold is precious. 
A. All Y is Z = All gold is a mineral. 
I. Some Z is X = Some mineral is precious. 

If this conclusion be not true, then must its contradictory, 
No Z is X = No mineral is precious, 

be so. Substituting this as the major premiss in the syllo- 
gism, we have 

No Z is X = No mineral is precious. 

All Y is Z = All gold is a mineral. 

From which we draw the new conclusion 

No Y is X = No gold is precious. 

But this conclusion is false, because it is the contrary of the 
original major premiss, which we assume to be true ; one of 
the premisses from which it was derived must be therefore 
false : it cannot be the minor, which was also assumed to be 
true ; it must, therefore, be the major, which is the contradic- 
tory of the original conclusion ; hence, the original conclu- 
sion must be true. 

It will occur, in reducing many of the moods by this pro- 
cess, as in the last example, that we shall find the conclusion 
false, because it is the contrary and not the contradictory of 
one of the original premisses. By referring to the subject of 
Opposition (30), we see that if one contrary is true the other 
must be false. 

Without presenting a greater number of examples of this 
kind of reduction, which the student may multiply for him- 
self, we lay down the following rules for reducing the various 
imperfect moods. 

Mules for Indirect Reduction. 
1st". In the second figure, substitute the contradictory of the 
conclusion for the minor premiss, and proceed as above in the 
mood Fakoro. 



INDIRECT REDUCTION. 



113 



2d. In the third figure, substitute the contradictory of the 
conclusion for the major premiss, and proceed as with the 
mood Darapti. 

3d. In the fourth figure, substitute the contradictory of the 
conclusion for the minor premiss, and proceed as before.* 

As reference is always easier to a tabular form, we annex 
one showing in what perfect mood the indirect reduction of 
each imperfect mood will take place : 



Fig. II. 


Fig. III. 


Fig. IV. 


Cesare to Ferio. 


Darapti to Celarent. 


Bramantip to Celarent. 


Carnestres to Darii. 


Disarms to Celarent. 


Camenes to Darii. 


Festino to Barbara. 


Felapton to Barbara. 


Dirnaris to Celarent. 


Fakoro to Barbara. 


Datisi to Ferio. 


Fesapo to Celarent. 




Dokanio to Barbara. 


Fresison to Celarent. 




Feriso to Darii. 





Before proceeding to consider the irregular, informal and 
compound syllogisms, we pause to show the method of geo- 
metrical notation, already referred to, by which the pure 
syllogism may be expressed. 

(42.) Notation of the Syllogism. 
As there subsists in the mathematics such a relation of 
analysis to geometry, as that most analysis is capable of geo- 
metrical construction, and every form of geometry may be 
stated analytically in terms of its equation, so mathematical 
logicians have attempted to make for the analysis or symbolic 
form of the syllogism such a geometrical notation as shall at 
a glance represent to the eye, in areas of limited space, what 
the symbols do to the mind. Indeed, the idea is so simple 
that we have already illustrated the dictum of Aristotle 
through its agency. Many writers, however, have been in- 
clined to go too far in its use. 

* Except in cases, of Bramantip and Dirnaris, in which the contradic- 
tory is substituted for the major premiss, and the conclusion simply con- 
verted. 

10* H 



114 LOGIC. 

The schemes of notation best known are those of Euler, 
Ploucquet and Lambert, and the more complete one of Sir 
William Hamilton. This latter, however, passing beyond 
our needs, is suited to such changes as would result from the 
introduction of the new analytic; and, as we have advisedly 
declined to place that system in our text-book, it is sufficient 
to mention Sir W. Hamilton's scheme without explaining it. 
In a more extended historical treatise it would demand a 
special consideration. We can here only explain what we 
mean to use. 

Euler's scheme of notation is altogether the one best suited 
to our purpose, and we shall limit ourselves to the explanation 
of that. It is essentially an arrangement of three circles, to 
represent the three terms of a syllogism, and, by their com- 
bination, the three propositions. Thus, if we have the judg- 
ment 

All men are mortal, 

we know that under this class — all men — are included many 
species and individuals ; as, for example, all Americans. Rep- 
resenting, then, the sphere of the conception mortal by a circle, 
placing within this circle a smaller one, wholly contained in 
it, as the sphere of all men, and yet a smaller one, wholly 
contained in this latter, as the sphere of all Americans, we 
shall have — 




which is the notation of a syllogism in BArbArA. By 
similarity of process, we shall represent the syllogism in 
CElArEnt: 



INDIRECT REDUCTION. 



115 



No A is B, 
All C is A, 
No C is B. 





DArll will be thus expressed : 




All A is B, 
Some C is A, 
Some C is B. 



Here it is evident that it is only that some C ichich is contained 
in A that we have a right to assert is also contained in B, 
although other portions of C may by chance be also contained 

in B. FErlO : 

No A is B, 
Some C is A, 
Some C is not B. 





Here two cases are presented — where no C is B and where 
some C is B — neither of which affects the truth of the conclu- 
sion that some C is not B. We have only applied this scheme 
to the first figure, but by this simple notation of Euler every 
syllogism in the other figures may be represented to the eye, 
and made clear to those who are much quicker at geometry 



116 



LOGIC. 



Take for example Darapti of the 




than at analytical work, 
third figure : 

All A is B, 
All A is C, 
Some C is B. 



But besides this representation of valid syllogisms, this 
system exposes at once fallacious arguments and acts as a 
test upon a test of their unsoundness. Take for example the 
case of illicit process of the major term : 



All quadrupeds are animals, 
A bird is not a quadruped, 
A bird is not an animal. - 



In which the figure denies the conclusion by allowing the 
premisses, and yet showing that birds are contained under 
the genus animal. Or if we take the case of the negative 
premisses : 

No A is B, 

No C is A, 





the figure shows us that there is no relation whatever estab- 
lished between or among the terms which would entitle us to 
a conclusion. 

The student will find it easy aud pleasant to write out all 
the moods and the logical fallacies by this circular method 



INDIRECT REDUCTION. 117 

of notation ; and as two modes of coming at facts make the 
memory more tenacious of them, this practice will fix clearly 
in his mind the moods and figures of the syllogism. 

The system also illustrates the categorical propositions as 
to the distribution of their terms, very satisfactorily : 



No A is B, 
Some A is B, 

Some A is not B. 

It would be a good exercise for the student to be called 
upon to represent any given syllogisms by this notation. 




CHAPTER IX. 

OF IRREGULAR, INFORMAL AND COMPOUND ARGU- 
MENTS. 

(43.) Of Abridged Syllogisms. 

We have thus far considered only those arguments which 
appear directly and without analysis in the form of a simple 
syllogism, and have explained those processes which we per- 
form upon known and acknowledged facts, stated as prem- 
isses and conclusion ; but the mind of man sometimes passes 
intuitively over certain steps of these processes without stop- 
ping to express them, which gives rise to abridged arguments ; 
or it halts in doubt and uncertainty, being not sure of its 
facts, but frequently balancing between two, one of which 
must be true, because of the truth or falsity of the other. 
This produces hypothetical syllogisms. 

All these in the present chapter will be treated of as in- 
formal syllogisms, or arguments which are not syllogisms in 
form, but which, if they be valid, must be capable of being 
put into the syllogistic form. 

The first of the abridged arguments to be considered, be- 
cause the one in most common use, is 

The Enihymeme* 

The enthymeme is a syllogism with one premiss suppressed, 
it matters not which ; thus, having the syllogism : 

All men are mortal, 
Caesar is a man, 
Caesar is mortal, 

* evOvfieopcu, to conceive in the mind. 
118 



OF ABRIDGED SYLLOGISMS. 119 

we may suppress the major premiss and write the enthy- 

meme, 

Csesar is a man. 
Therefore Csesar is mortal. 

Or, suppressing the minor premiss, we have, 

All men are mortal, 
Therefore Csesar is mortal, 

either of which is a satisfactory expression, because all three 
terms of the syllogism are expressed in either form of the en- 
thymeme, and we can at once reconstruct the syllogism ; thus, 
taking the latter form, with the minor premiss suppressed, we 
see by examining the conclusion, in which the major and 
minor terms are always contained, that Ccesar is the minor, 
being the subject of the conclusion, and mortal the major, 
being the predicate. Men, then, must be the middle term, 
and we at once compare it with the minor term to form the 
suppressed premiss ; thus, 

Csesar is a man. 

By a similar process we may reconstruct the syllogism when 
the major premiss is suppressed. 

It is worthy of observation that in ordinary discourse men 
suppress the major premiss habitually, as that to which the 
mind most readily yields assent, although, if the proof of its 
truth be required, the task would be more difficult than to 
establish the truth of the minor. Thus, in the example 
given above, we would take for granted as a fact that 

All men are mortal ; 
whereas, without the declarations of the Bible — and Logic, 
as a science, moves independently of any extraordinary or 
supernatural dicta — this proposition is incapable of proof; 
for, although all men have died thus far in the world's his- 
tory, the process of induction cannot be finished until the 
end of man as a race. 

But this seems like a cavil. The major premiss, although 



120 LOGIC. 

thus incapable of mathematical proof, is the one which most 
surely demands belief; and so, when in the enthymeme we 
speak of the suppressed premiss, we mean the major premiss, 
unless it be otherwise explained. 

As a simple rule for reconstructing the syllogism from the 
enthymeme, we observe that, 

If the subject of the conclusion be found in the expressed 
premiss, that premiss is the minor. If the predicate of the 
conclusion be found in the expressed premiss, it is the major. 

Sometimes it becomes necessary to put the enthymeme into 
logical form before proceeding to reconstruct it. Thus, the 
example given above might be, and most commonly is, thus 
spoken or written : 

Caesar is mortal, 
Because Caesar is a man ; 

which is evidently a transposed form of the enthymeme. 
Whenever the causal conjunction because unites the proposi- 
tions of an enthymeme, we may invert the propositions and 
unite them with the illative conjunction therefore, and then 
proceed to reconstruct the syllogism ; thus, 

Caesar is a man, 
Therefore He is mortal. 

Many abridged arguments which appear in a hypothetical 
form are in reality simple enthymemes ; thus, 

If murder is a crime, 

The murderer should suffer. 

In which there is really no hypothesis or condition in the 
premiss, because all allow that murder is a crime, and are 
consequently ready to declare that 

The murderer should suffer. 

When the enthymeme has been reconstructed into a syllogism 
in any one of the figures, we shall be able to put it directly 
into the first figure, and can then apply to it the test of Aris- 
totle's dictum. 



THE SORITES OR CHAIN ARGUMENT. 



121 



(44.) The Sorites* or Chain Argument. f 
The Sorites is an abridged argument consisting of a series 
of propositions in which the predicate of the first is the subject 
of the second, the predicate of the second the subject of the 
third, and so on until we combine the subject of the first and 
the predicate of the last to form a conclusion ; thus, 

A is B = The mind is a thinking substance. 

B is C = A thinking substance is a spirit. 

C is D = A spirit has no composition of parts. 

D is E = (That which has) no composition of parts is indissoluble. 

E is F = (That which is) indissoluble is immortal. 

Concl. A is F = The mind is immortal. 

This may be illustrated by a figure : 




Now, if we try to put this collection of abridged arguments 
into the syllogistic form, in order to apply the dictum of 
Aristotle to them, we shall see that the Sorites is an abridg- 
ment of a series of syllogisms in the first figure ; that the 
terms B, C, D and E, which are used twice, are middle terms, 
and that we may construct as many syllogisms as we have 
middle terms. Taking, then, the second proposition of the 
sorites, B is C, as the major premiss of the first syllogism, 

* aopeiTTig = a heap, or collection. 

f Called by the Germans, more significantly, Kettenschluss, or chain 
argument. 
11 



122 LOGIC. 

and the first, A is B, as the minor, we shall have as a conclu- 
sion A is C, which we use as the minor premiss of a second 
syllogism, using the third proposition of the sorites as a major 
premiss ; and so on, as long as the middle terms last ; thus, 



1st. 


2d. 


3d. 


4th. 


BisC, 


CisD, 


DisE, 


EisF, 


AisB, 


AisC, 


AisD, 


AisE, 


AisC. 


AisD. 


AisE. 


AisF. 



A thinking substance is a spirit. 
1st. The mind is a thinking substance. 
The mind is a spirit. 

A spirit has no composition of parts. 
2d. The mind is a spirit. 

The mind has no composition of parts. 

That which has no composition of parts is indissoluble. 
3d. The mind has no composition of parts. 
The mind is indissoluble. 

That which is indissoluble is immortal. 
4th. The mind is indissoluble. 
The mind is immortal. 

These are all in the first figure, and consequently are forms 
to which the dictum will directly apply. 

It must be observed that in the sorites the first proposition, 
A is B, is the only one which may be particular, because it 
is the only minor premiss expressed, every other being used 
as a major, and we have already seen that in the first figure 
the major premiss must be universal. 

So, again, the last proposition, E is F, is the only one that 
may be negative, for, if any other be negative, we should have 
in one of the syllogisms a negative conclusion which is to be 
in turn the minor premiss of the succeeding syllogism, and we 
have already shown that in the first figure the minor premiss 
must be affirmative. But the. conclusion deduced from the 
last syllogism does not become a minor premiss, and so the 
last conclusion may be negative ; it would then read thus : 



THE SORITES OR CHAIN ARGUMENT. 123 

No E is F. 
All A is E. 
No A is F. 

Or the chain of the sorites would be broken in whatever place 
the negative proposition should occur. 

The sorites is a very simple and conclusive abridged form 
of argument ; for the mind, taking the only expressed minor 
term A, which is expressed in the chain, links it by jumping 
from middle term to middle term, B, C, D, E, to the final 
major term or F, as surely and more easily than in the syllo- 
gisms into which it is elaborated. 

By its aid we easily establish the points in any great argu- 
ment, either as recapitulating the process of the argument, or 
as stating them preparatory to a comprehensive discussion. 
Thus, to establish the effect of a republican government, we 

shall have — 

The Americans make their own laws. 
Those who make their own laws are free. 
Those who are free are contented. 
Those who are contented are happy. 
Therefore The Americans are happy. 

It is evident that the sorites may be properly stated in the 
inverse order, thus : 

DisE, CisD, B is C, A is B, 
Therefore A is E. 

Here the sorites starts from its widest terms, D and E, to 
include the narrower and more limited terms, C, B, and 
finally A. 

This form is called the Goclenian Sorites, from the name of 
its originator. It serves, perhaps, better to illustrate the fact 
stated that only the most extensive proposition, which in the 
ordinary form is the last, and in this the first, may be nega- 
tive ; which, as we have seen, will give us a negative conclu- 
sion, thus : 

D is not E, C is D, B is C, A is B, 

Therefore A is not E. 



124 LOGIC. 

Hypothetical Sorites. 
If we have a string of conditional propositions, such that 
the consequent of each becomes the antecedent of the succeed- 
ing one, the argument is called a hypothetical sorites, and the 
conclusion is obtained either by affirming the first antecedent 
with the last consequent, or by denying the last consequent 
with the first antecedent, thus : 

1. If A is B, C is D; If C is D, E is F; 

But A is B, Therefore E is F. 

2. If A is B, C is D ; If C is D, E is F ; 
But E is not F, Therefore A is not B. 

Examples. 
1. 
If the Bible is from God, it should be taught ; 
If it should be taught, men should be set apart to teach ; 
If men should be set apart to teach, they should be supported ; 
But the Bible is from God, therefore its teachers should be supported. 

2. 
If the Bible is false, it deceives the world ; 
If it deceives the world, it should be destroyed ; 
But it should not be destroyed, therefore it is not 



To the hypothetical sorites it is evident that the Goclenian 
form will also apply. Indeed, this is illustrated in the last 
case mentioned, where we reason back from the denial of the 
last consequent to the denial of the first antecedent. 

(45.) Of the Epichirema.* 

Most arguments employed in ordinary conversation and 

writing consist of simple syllogisms, abridged into enthy- 

memes, linked together in a compound form ; but in many cases 

the form of the syllogism is observed where the premisses are 

* The Greeks seem to have considered this a great logical weapon, 
as the name they gave it signifies a violent onset or laying of hands upon. 
Eiri and x E ' l P* 



OF THE EPICHIREMA. 125 

arguments in themselves. "When the premisses are thus sepa- 
rately established, before the conclusion is deduced, the argu- 
ment is called an Epichirema, thus : 

The victors are injured by war, because it hardens their hearts ; 
The French were victors at Marengo, for they retained the jield; 
The French were injured by their victory. 

The major premiss is an enthymeme, which may be ex- 
panded into a syllogism ; the same is true of the minor ; hence 
we have two distinct arguments within the one which origi- 
nally appeared. To apply the tests to their validity, they 
need only be written out in syllogistic form. In most ap- 
parently simple syllogisms there is in reality implied the 
epichirema. As for example, in the one given to illustrate 
the mood Fakoro, of the second figure, 

All true patriots are friends to religion, 

Some great statesmen are not friends to religion, 

Some great statesmen are not true patriots, 

the major premiss demands in itself a reason, thus : 

All true patriots are friends to religion, because religion is the basis of 
national prosperity and advancement. 

So also does the minor, 

Some great statesmen are not friends to religion, because their own lives 
are not in accordance with its precepts. 

Each of the premisses given is an enthymeme; of which 
the clause because, etc. is the premiss, and the first statement, 
all true patriots, etc., is the conclusion. Now, this premiss 
to the premiss is called the prosyllogism. 

Sometimes the establishment of the final conclusion will 
warrant us in drawing other conclusions also, thus : 

AisB, 

C is A, 
Therefore C is B, 
Therefore X is Y, etc. 
11* 



126 LOGIC. 

This conclusion from a conclusion (X is Y) is called the epi- 
syllogism. 

In mathematics it is called a corollary, or something that 
flows from the demonstration without new proof 

To take the example before quoted, we shall have : 

All true 'patriots are friends to religion. 
Some great statesmen are not friends to religion. 
Some great statesmen are not true patriots. 
Therefore They deceive their countrymen, 

and Deserve no rewards from their country, etc. 

A number of syllogisms joined together in a connected 
argument constitutes a Poly-syllogism. 

(46.) Of Hypothetical Syllogisms. 

Corresponding to the various forms of hypothetical proposi- 
tions — viz., conditional, causal, disjunctive, etc. — we have con- 
ditional, disjunctive and causal syllogisms. They are all of so 
simple a nature that the mind finds no difficulty in the ratio- 
cination which they express ; but as we have asserted that, if 
valid, they may be reduced to the form of a categorical syllo- 
gism in the first figure, we proceed to show how this may be 
done. 

Conditional Syllogisms. 

If we examine a conditional proposition, we shall see at once 
that the affirmation of the consequent will follow from the 
affirmation of the antecedent ; thus : 

If A is B, C is J) = If he has a fever, he is sick. 

But if we deny the antecedent, we may not therefore deny the 
consequent, since this consequent might spring from some 
other antecedent as well as from the one given, thus : 

If A is not B = if he has not a fever, 

we cannot say, 

C is not D = he is not sick, 
since 



OF HYPOTHETICAL SYLLOGISMS. 127 

C might be D — he might be sick, 
from some other cause than 

A being B, or his having a fever. 

For similar reasons we may pass from the denial of the 
consequent to the denial of the antecedent, but not from the 
affirmation of the consequent to the affirmation of the antecedent. 
When we pass from the affirmation of the antecedent to the 
affirmation of the consequent, the reasoning is called constructive ; 
and when we pass from the denial of the consequent to the 
denial of the antecedent, it is called destructive. 

We may have, then, two, and only two, forms of conditional 
syllogisms, constructive and destructive. To form the first, we 
take the whole conditional proposition as the major premiss ; 
the affirmation of the antecedent for the minor, from which 
premisses we shall draw the affirmation of the consequent as 
the conclusion, thus : 

Maj. prem. If A is B, C is D = If he has a fever, he is sick. 
Min. prem. A is B = He has a fever. 

Conclusion. C is D = He is sick. 

To frame the destructive conditional syllogism, we take the 
whole proposition as before for a major premiss, the denial of 
the consequent for a minor, and we deduce as a conclusion the 
denial of the antecedent, thus : 

Maj. prem. If A is B, C is D = If he has a fever, he is sick. 
Min. prem. C is not D = He is not sick. 

Conclusion. A is not B = He has not a fever. 

As these are the only possible forms of conditional syllo- 
gisms, and as we have shown that all other forms of hypo- 
thetical propositions — disjunctive, causal, etc. — may be easily 
reduced to conditional propositions, we have only to show how 
these conditional syllogisms may be reduced to the form of 
simple categorical syllogisms, and we shall, in effect, have 
shown it for all. 

Considering first the constructive form, and remembering 



128 LOGIC. 

that the form of condition may be removed by the phrases 
" the case of" and " the -present ease" and that the proposition 
assumes the form of a categorical proposition, of which the 
antecedent becomes the subject, and the consequent becomes a 
predicate, we shall have for the constructive form, 



j. prem. The case of A being B is the case of C being D. 
Z X 



Min. prem. The present case is the case of A being B. 
Z Y 



Concl. The present case is the case of C being D. 

Or, All X is Y. (A) 
All Z is X. (A) 
All Z is Y. (A) 

which, X being the middle term, is evidently in the first 
figure, and the dictum may be at once applied. Using the 
same phraseology, and thus translating the destructive form, 
we have, 



The case of A being B is the case of C being D. 
Z Y 



The present case is not the case of C being D. 
Z X 



The present case is not the case of A being B. 

Or, All X is Y. (A) 
No Z is Y. (E) 
No Z is X. (E) 

which, Y being the middle term, is in the second figure, and 
in the mood Camestres, which must be reduced to the first 
figure or the form of the dictum. 

If, now, we perform the operations indicated to reduce this 
mood (m, s, s), we simply convert the minor premiss, and then 



OF HYPOTHETICAL SYLLOGISMS. 129 

transpose the premisses, and simply convert the conclusion : 

we shall have, 

Y Z 



The case of C being D is not the present case. 
X Y 



The case of A being B is the case of C being D. 
X Z 



The case of A being B is not the present case. 
or simply converting the conclusion, 



The present case is not the case of A being B. 

No Y is Z. (E) 
All X is Y. (A) 
NoXisZ. (E) 



or, No Z is X. 

which is the form of Celarent in the first figure. 

The logical form of the conditional does not depend upon 
the subject-matter of the propositions composing it. There 
may be, for example, two apparently independent proposi- 
tions — that is, propositions in which the terms are entirely 
distinct — thus conjoined, or there may be a term the same in 
each, which will cause no difference in the logical form ; thus 
we may have — 

If A is B, C is D = If John remain, James will go ; or, 
If A is B, A is C = If the Bible is true, it (the Bible) deserves our 
attention. 

To explain this apparent difference, it will be remembered 
that A, B, C, elc, although terms in the proposition, are not 
the terms of the syllogism when it is put in a categorical 
form, but that the antecedent and consequent become the true 
terms ; and therefore it matters not whether there be three or 
four independent terms in the conditional proposition before 
its change of form. 

I 



130 LOGIC. 

A few examples of conditional syllogisms are given to 
accustom the student to the form, and to guard him against 
the improper use of it. 

Examples. 
1. 
If the fourth commandment is obligatory upon us, we are bound to 
set apart one day in seven. 

But the fourth commandment is obligatory upon us. 
Therefore we are bound to set apart, etc. 

2. 

If any theory could be framed to explain the establishment of Chris- 
tianity by human causes, such a theory would have been proposed 
before now. 

But none has been proposed. 

Therefore no such can be framed. 

3. 

If the eclipses of Jupiter's moons occur sixteen minutes later, when 
the earth is farthest from Jupiter, than when she is nearest to Jupiter, 
light must travel ninety-five millions of miles in eight minutes. 

But these eclipses do occur so much later in the given position. 

Therefore light travels at the rate stated, or, two hundred thousand 
miles in a second. 

4. 

If taste is uniform, all men will admire the same objects. 

But all men do not admire the same objects (one sees beauty where 
another only finds deformity). 

Therefore taste is not uniform. 

Disjunctive Syllogisms. 
A disjunctive syllogism is one the major premiss of which 
is a disjunctive proposition (26), and the minor a categorical. 

Brutus was either a parricide or a patriot = Either A is B, or it is C. 
He was not a parricide = A is not B. 

He was a patriot = A is C. 

Here, when the major premiss consists of two members 
only, the minor asserts the one and the conclusion denies the 
other ; or, the minor denies the one and the conclusion asserts 



OF HYPOTHETICAL SYLLOGISMS. 131 

the other. Or we may have, instead of two alternatives, 
three or more, thus : 

The angle A must be equal to, or greater or less than, the angle B. 
But it is neither greater nor less than it. 
Therefore it is equal to it. 

It is evident that the disjunctive syllogism may be at once 
stated in a categorical form by any simple phraseology which 
will rid us of the disjunctive form, thus: 

Brutus could not be at the same time a parricide and a patriot (but 
must be one of the two). 
He was a patriot, 
Therefore he was not a parricide. 
Or, He was not a parricide, 
Therefore he was a patriot. 

Examples of Disjunctive Syllogisms. 
1. 
It is either true that knowledge is useful, or that ignorance is so. 
But it is not true that ignorance is useful. 
Therefore knowledge is so. 

2. 

Mohammed was either an enthusiast or an impostor. 

He was an enthusiast. 

Therefore he was not an impostor. 

This is Gibbon's argument, but it is faulty in point of fact, 
for a man may be both enthusiast and impostor, and some 
men have a great enthusiasm for imposture. 

3. 

A government either licenses a free press, or it is oppressive. 
The French government does not license a free press. 
Therefore it is oppressive. 

4. 

A wise lawgiver must either recognize future rewards and punish- 
ments, or must appeal to an extraordinary Providence. 
Moses did not do the former. 
Therefore he must have done the latter. 



132 



LOGIC. 



Of the Dilemma, Trilemma, etc.* 
A dilemma is a compound argument composed of condi- 
tional propositions upon which we reason disjunctively. 
When two conditional propositions are combined with a dis- 
junctive minor premiss, the argument is called a dilemma. 
When three, four, etc. are so combined, they constitute a 
trilemma, tessaralemma, etc. The generic name Dilemma, 
however, is technically given to them all. Dilemmas are 
divided into four kinds, according to their being simple or 
complex, constructive or destructive. 

A simple dilemma is one in which we have as a major pre- 
miss several antecedents with a single consequent, thus : 



Maj. prem. 



If A is B, 

If C is D, then X is Y, 

If E is F. 



Min. prem. -{ 



{ But either 


AisB 


i or 


CisD 


or 


EisF 



Conclusion. Therefore X is Y. 



A complex dilemma is one in which we have several ante- 
cedents, and each has its own consequent, thus : 



If A is B, G is H. 
Maj. prem. -{ If C is D, I is K. 

If E is F, L is M. 



Min. 



prem. 



Either 
AisB 

or 
CisD 

or 
L EisF 



Conclusion. Therefore - 



f Either 
GisH 

or 
IisK 

or 
LisM 



Now, if in the simple dilemma, instead of reasoning as we 
have done constructively from the disjunctive affirmation of the 
* Sic; rpeiQ, reocapeg, etc., and /W///za, from Xa/i(3avo). 



OF HYPOTHETICAL SYLLOGISMS. 133 

antecedents to the disjunctive affirmation of the consequent, we 
reason destructively — that is, deny the single consequent — then 
all the antecedents fall to the ground ; there is no longer the 
condition of the dilemma ; for we have a simple conditional 
syllogism. Or if we have one antecedent and several conse- 
quents, and reason destructively, it is as though we had but one 
consequent, since the denial of any one requires the denial of 
the one antecedent; thus, in the argument, 

f C is D, 

If A is B, -j G is H, 

[LisM, 

it matters not whether we deny one or all the consequents, the 
denial of the antecedent follows. Hence, properly speaking, 
there is no such thing as a simple destructive dilemma. It dif- 
fers in no wise from a simple destructive conditional syllo- 
gism. 

The destructive dilemma proper, then, consists of several 
antecedents, each with its own consequent, in which we disjunc- 
tively deny the consequents — that is, deny any of them or all in 
turn — and we may disjunctively deny the antecedents. 

If A is B, CisD. „. But either C is not D 

Maj.prem. ^ G is H L is M Mm. prem. or L . g not M 

etc. etc. 

Conclusion. Therefore either A is not B, 
or G is not H. 

To apply this abstract form to a particular example; let us 
take the argument of Antisthenes : 

If we conduct the affairs of state well, we offend men. 
a J- P r - jf we cono l uc t them ill, we offend the gods. 

If now we reason constructively we shall add, 

But, we must either conduct them well, 
Min.prem. or conduct them ill. 

Conclusion. Therefore we must either offend men, 
or offend the gods. 
12 



134 LOGIC. 

If we reason destructively, we add, as a minor premiss, 

But we must either not offend men, or not offend the gods, 

and as a conclusion, 

Therefore, we must either not conduct them well, or not conduct 
them ill. 

To rid themselves of the perplexities of the dilemma, the 
old logicians always established from their premisses an un- 
due, because not a logical, conclusion, but a moral and mate- 
rial one, a passage of the mind to a purpose which had been 
suggested by the matter of the argument ; thus, the conclu- 
sion of Antisthenes from the perplexity of the dilemma was, 
that we had better not meddle with the affairs of state at all. 
Take another illustration: 

If a wife is beautiful, she excites jealousy ; 
If she is ugly, she gives disgust; 

and the illogical but common conclusion is 

It is best not to marry. 

Most logicians have erred at the very outset by supposing 
that, because there is an alternative expressed in the dilemma, 
it is a disjunctive instead of a conditional syllogism, and thus 
have rendered it a vehicle of fallacy which it would be im- 
possible for Logic to arrest ; thus, they would read the last 
example, 

Either a wife excites jealousy by her beauty, 

Or disgust by her ugliness ; 

Hence it is better not to marry. 

In any such case, if we first put the dilemma in its true 
conditional form, and then (leaving the province of Logic, 
which presumes all given propositions to be true) examine 
the subject-matter of the propositions themselves, we shall find 
the falsity which causes perplexity ; thus, it is not true univer* 



OF HYPOTHETICAL SYLLOGISMS. 135 

/, nor commonly, as is implied in the example, that if a 
wife is beautiful she excites jealousy. It is even less true, that 
is, in a fewer number of cases, that if she is ugly she causes 
disgust; hence the conclusion that it is best not to marry is 
less true, i. e., applies to a fewer number of cases, than either 
of the foregoing assertions, i. e., the falsehood is increased by 
the number of false statements preceding the conclusion. 

It is evident that the dilemma may be resolved into as 
many conditional syllogisms as the greatest number of ante- 
cedents or consequents, and that these may be reduced ac- 
cording to the rules for the reduction of conditional syllo- 
gisms. 

Any dilemma may also be stated in a categorical form. 
Thus, 

The case of A being B, is the case of G being H, 
The case of C being D, is the case of E being F ; 

and we may then proceed as in conditional syllogisms. 

Examples of the Dilemma. 
1. 
If Eschines joined in the public rejoicings, he was inconsistent. 
If he did not, he was unpatriotic. 
But either he did join, or he did not. 
Therefore, he was either inconsistent or unpatriotic. 

The following dilemma was formed to confute the doctrine 
of Pyrrho, the skeptic, which was, that because everything 
has its contradictory, everything is false; or that no one could 
know anything certainly : 

2. 

If what you say is true, then there is something which is not false ; 
ergo, your system is wrong. 

If what you say is false, then it has no value as an argument ; i. e., 
your system is wrong. 

But what you say must be either true or false. 

Therefore, in either case your system is wrong. 



136 LOGIC. 

3. 

There are two kinds of things which we ought not to fret about — 
what we can help and what we cannot. 

(The student will put this in the form of a dilemma.) 

Having explained the various forms of argument, simple 
and compound, our next subject of investigation is of the 
erroneous use of these forms. To this has been given the 
generic title of Fallacies. 



CHAPTEK X. 

FALLACIES. 

(47.) The Meaning and Comprehension of a Fallacy.* 

Different terms are used to express the errors which are 
found in terms, propositions or arguments in Logic. Thus/we 
say of a term, when it is not uni-voeal, i. e., when it has not 
one meaning and only one, that it is equivocal or ambiguous, 
i. e., has more than one meaning ; of a proposition, if it be not 
true, that it is false, which expresses in other words that the 
predicate and subject have no proper connection ; of an argu- 
ment we say, when it violates the dictum of Aristotle or any 
of the rules given, that it is invalid, and sometimes of an in- 
valid argument we say that it is fallacious. 

A fallacy, then, is an invalid argument which appears at first 
sight to be valid. If it be used with the intention to deceive, the 
fallacy is called a sophism.f An argument manifestly and 
foolishly invalid would then be neither a sophism nor a fal- 
lacy. 

The subject of fallacies is one of the most important in the 
study of Logic, for not only is Logic designed to teach us to 
reason correctly, but also it should teach us to perceive and 
detect all errors in reasoning. Hence we find the earliest 
writers on Logic giving rules and cautions for avoiding and 
detecting fallacies. 

The first division of fallacies which they have made is into 

* Folio = to deceive. 

f Sophism comes through the word ZoQkttijc, from go^os, wise. Sophist 
was the name given in irony to those whose wisdom showed itself in an 
abuse of words and reasoning. 

12 * 137 



138 LOGIC. 

fallacies in dictione and extra dictionem. As dictio means 
the form of words, and not the meaning of the words, or 
what is expressed in our word diction, the class in dictione, 
or fallacies in form, will evidently come within the province 
of Logic, while those extra dictionem, not being in the form, 
but in the subject-matter, with which Logic is only indirectly 
concerned, will really not fall within the scope of our study. 
But since the line between the two, although easy to be 
drawn, is continually mistaken in practical argument or con- 
troversy unless it be thus drawn, it becomes necessary to 
explain both classes with care, that we may always distinguish 
between the truly Logical and the non-Logical or material 
fallacies; and this is particularly important, because those 
who resort to fallacious reasoning use both these kinds of 
fallacy in combination with each other. One class of these 
material fallacies, which arises from the ambiguity in words, 
and is therefore called verbal fallacies, needs but a slight 
change, as we shall see, to become formal or logical fallacies. 

(48.) Of Fallacies in Dictione, or Formal Fallacies. 

These are the fallacies about which Logic is particularly 
concerned. 

Under this class are included all violations of the dic- 
tum of Aristotle, and of the axioms and rules laid down for 
determining the validity of an argument. The fallacy in 
all cases under this head is apparent in the form of the ex- 
pression ; hence the name formal fallacies. Of this kind are — 

1. Undistributed middle terms. 

2. Illicit process of either term. 

3. Negative premisses. 

4. Affirmative conclusion from a negative premiss, and 
vice versa. 

5. More than three terms in the argument. 

Of these, repeated examples have been already given in 



OF FALLACIES IN DICTIONE, OR FORMAL FALLACIES. 139 

syllogistic form ; it is only by putting them in this form that 
the fallacy is at once and easily detected. 

But it should be borne in mind that in practice such falla- 
cies are not stated in the syllogistic form, in which they are 
thus easily to be detected, but are stated in the form of an 
enthymeme, or other abridged argument, and so covered with 
words that the effect is produced without the mind being con- 
vinced — the conclusion allowed, because the mind cannot see 
the false steps which have been used, although it has not cer- 
tified itself that the true have been taken. Let the student 
then take the trouble, in each such case, to write out the 
argument in syllogistic form, and, for greater clearness, to use 
symbols, and the invalidity will be apparent. 

Thus, we are told that " a certain man was a good father, 
because he attended to the physical necessities of his chil- 
dren ;" food and clothing and shelter being the criterion of a 
good father. Let us apply the test of Logic to such an 
argument : 



X Y 



Maj. prem. 



All good fathers provide for the physical wants of 

their children. 



Min. prem. A B did thus provide 
Z X 



Therefore A B was a good father. 

Or, using symbols, 

AllXisY, 
ZisY, 
ZisX. 

That is, Y, which is the middle term, is undistributed, being 
the predicate in two affirmative premisses. 

Again, it is asserted that "brutes are not accountable beings, 
because they are not responsible ;" which involves a fallacy 
of illicit process. Thus, 



140 LOGIC. 

X 



Maj. prem. All responsible beings are accountable. 
Z X 



Min. prem. Brutes are not responsible beings. 
Z Y 

Therefore Brutes are not accountable. 

All X is Y, 
No ZisX, 
No ZisY. 

In which Y, which is distributed in the conclusion — being 
the predicate of a negative proposition — is undistributed in 
the major premiss : an illicit process of the major term. 

It will be observed, in this latter instance, that the conclu- 
sion is, we believe, a true one, but it is not reached by such 
premisses ; and thus indeed it constantly happens, that men 
adopt a conclusion on internal grounds which they cannot 
explain, and then seek in every direction for premisses by 
which to substantiate it : and so, on the other hand, many a 
just statement loses credence, from the fact that weak and 
empirical men undertake to prove it by false premisses or 
fallacious reasoning. 

It is further to be remarked that men who are guilty of 
fallacy in argument, either through design to deceive or 
weakness of reasoning power, are apt to combine many single 
arguments into a compound argument. If, then, one of these 
be faulty in its ratiocination, every ulterior conclusion is en- 
dangered, and the whole chain of argument is fallacious. To 
detect the error, therefore, requires that the whole chain be 
exposed link by link, and that the proper tests be applied to 
each argument. We have given examples of the fallacy of 
undistributed middle and illicit process; the student will not 
need illustrations of the other formal fallacies mentioned. 



MATERIAL, OR INFORMAL FALLACIES. 141 

(49.) Material, or Informal Fallacies. 

It will be allowed that in every fallacious argument the 
conclusion does or does not follow from the premisses. If it do 
not follow from the premisses, then when written out by sym- 
bols the fallacy is apparent, coming under one of the heads 
of formal fallacies which we have just enumerated. The fault 
here is evidently in the reasoning ; but when the conclusion 
does follow from the premisses, when written out by symbols, 
the fallacy is not apparent, the fault will not lie in the reason- 
ing, but either in the premisses or in the conclusion, i. e., as to 
their truth or falsity, or as to the ambiguous meaning of words 
used in both. Such fallacies, with which Logic is not directly 
concerned, are called Material Fallacies. 

It has been remarked before that Logic indeed takes for 
granted that the propositions composing its syllogisms are 
true, and that, when we write the general proposition A is B, 
no meanings shall be given to A and B which shall violate 
the truth of the proposition. If then we put for A, Learn- 
ing, and for B, useless, and thus write, 



Learning is 

or, by a change of words, the doctrine of the Stoics, 
Pain is (a lesser sort of) pleasure, 

we shall reason to false conclusions, the matter of the prop- 
ositions forming the syllogism being false, while the logic of the 
argument may be correct. It must be allowed that material 
fallacies are more numerous and more fruitful causes of 
error than the logical, and as such deserve a special consid- 
eration, although indirectly allied to our subject. 

We shall, therefore, endeavor briefly to give the principal 
forms or titles of material fallacies, and to illustrate them by 
examples, observing, at the outset, that they assume many and 
varied forms under these titles, all of which we cannot take 
the time to consider. 



142 LOGIC. 

The simplest division of them is one which grows out of 
the consideration of — 

1. Errors in the premisses. 

2. Errors in the conclusion. 

Of Errors in the Premisses. 

Logicians have adopted technical names for the fallacies 
of this kind, viz. : the petitio principii, or begging the question; 
Arguing in a circle ; Non causa pro causa, or the assignment 
of a false or undue cause. These branch out into various 
minor divisions. 

As all these grow out of a false or undue assumption of 
premisses, they are akin to each other, and in many cases 
are not easily to be distinguished. Especially is this true of 
the first two. 

I. Petitio principii. This consists in using as a premiss to 
support an adopted conclusion or assertion the same fact in 
other words. Thus we are told that " if the heart be touched 
death ensues, because it is a vital part" or that "morphia pro- 
duces sleep because it is an anodyne." 

Now what is it to say but that death ensues when the 
heart is touched, because death doth ensue? or that morphia 
produces sleep because it produces sleep f 

Our language, which has so many synonyms from the Anglo- 
Saxon and the Latin, gives full play to this sort of fallacy, 
and many a wordy man is guilty of it without knowing his 
own error. And besides, this fallacy is the just recompense 
of those who endeavor to prove axioms, or who seek to pene- 
trate into the ultimate facts for which God assigns no cause 
but the fiat of his own will. 

II. Arguing in a circle. This fallacy depends upon find- 
ing a premiss to prove an asserted conclusion, and then, when 
asked for the proof of the truth of that premiss, endeavoring 
to make the conclusion prove the premiss ; or, as this would 
be easy of detection, to make the circle still larger — i. e., 



MATERIAL, OR INFORMAL FALLACIES. 143 

proving the truth of the premiss by a third proposition which 
depends upon the conclusion, and the playing upon these 
three, like the juggler's balls of which one is always in the 
air, but which, it is very difficult to tell. In case of the 
simplest form, writing out the syllogism will detect it ; and 
in the latter and more complex case, the sorites, or its syllo- 
gisms written out, will find it out. 

Thus, many men, not content with the everywhere shining 
proof within and without that there is a God, and mistaking 
the relations which the Holy Scriptures bear to him, would 
prove the existence of a God from the truth of the Scriptures, 
and then prove the inspiration of the Scriptures from the fact 
that they came from God. 

As the Scriptures are the word of God, what they declare must be true. 
The Scriptures declare that God exists. 
Therefore That God exists is true. 

Or again : 

The word of God must be true. 

The Scriptures are the word of God. 

The Scriptures are true. 

III. Non causa pro causa. This fallacy, which indeed 
may stand for the general title of unduly assumed premisses, 
consists technically in assigning as a reason or cause in the 
premisses one which has nothing to do with the conclusion, 
or one which is not itself proven, and is not therefore a suf- 
ficient cause. The first of these errors is called the fallacy 
of a non tali causa pro tali, or the assignment of a cause as 
though it were a cause, when it is not ; and the second is the 
a non vera pro vera, in which the assumed premiss cannot be 
proven to be true as a cause, and may therefore be consid- 
ered false. Under this head we have the fallacies technically 
called post hoc ergo propter hoc, or considering an event as a 
cause, because it precedes another event, and cum hoc ergo 
propter hoc, taking something for a cause when it occurs 
simultaneously with an event. 



144 LOGIC. 

Of the latter of these divisions, the a non vera, we find a 
striking example, and an excellent logical retort, in the 
reported dialogue between Charles II. and Milton, after the 
poet had become blind. " Think you not," said the king, 
" that the crime which you committed against my father must 
have been very great, seeing that Heaven has seen fit to pun- 
ish it by such a severe loss as that which you have sustained ?" 
" Nay, sire," Milton replied, " if my crime on that account be 
adjudged great, how much greater must have been the crimi- 
nality of your father, seeing that I have only lost my eyes, 
but he his head!" Another and common example of this is 
the following : 

The natives of barbarous countries regard an eclipse as 
portentous of war and famine ; and should they come together, 
they would assign it as the cause of their trouble. We 
know that it is not, but they only note the conjunction of the 
two as satisfactory proof that it is. Either of these may be 
easily written out in the syllogistic form, in which the propo- 
sitions can be scrutinized as to their subject-matter and the 
falsity detected. 

The fallacy of a non tali is chiefly used in analogous in- 
stances, where things which in one connection are useful or 
hurtful are assumed to be useful or hurtful in all ; a,s because 
dry weather is good for the traveler it is also good for the 
farmer, or because the corn-laws were beneficial to England 
at one time they must always be so. Of the a non tali, the 
following example will serve as an illustration, viz. : 
All poisons should be avoided. 
Brandy and wine are poisons. 
Therefore They should be avoided. 

That is, they are poisons only when taken in certain amounts 
and under certain circumstances. This is an invalid argu- 
ment used by many good persons, the true reason for avoid- 
ing brandy and wine being the danger of acquiring a habit 
of using them to such an extent that they will be poisons. 



MATERIAL, OR INFORMAL FALLACIES. 145 

Errors in the Conclusion. 

We come now to the second division of material fallacies — 
those in which the error lies in the conclusion ; they are all 
included under the general head of Ignoratio elenchi, or irrel- 
evant conclusion. ■ 

The word elenchus, as used in the early writers, meant the 
contradictory of your opponent's assertion, and thus implies, 
what indeed was a feature in earlier Logic, the existence of 
an opponent. Dialectics were almost always in the form of 
dialogue, and the Socratic mode of questions and answers 
was adopted as the acutest method of argument. 

The disputatious spirit of the Greeks was as much con- 
cerned about the victory in logomachy, or word-war, as about 
the discovery of truth, and hence arose many of their errors 
and paradoxes. This spirit of controversy and the constant 
keeping in sight of the elenchus has pervaded the methods of 
Logic to a very late period. 

The ignoratio elenchi is the ignorance of the contradictory of 
our opponent's assertion which we display when, instead of 
establishing the elenchus, i. e., proving the contradictory, and 
thus proving his conclusion or assertion false, we attempt to 
establish something resembling the contradictory. 

As it is not our purpose to reproduce the Grecian techni- 
calities and method, let us get rid of this name and form, and 
call the fallacy, as it has been called by modern writers, the 
fallacy of irrelevant conclusion. 

Those who employ it — and this, it may be remarked, is the 
most common and practical of all the material fallacies — 
generally state the conclusion as a fact, and when asked for 
the premisses or proof, are compelled to present such as dis- 
play the irrelevancy of the conclusion. Thus, one asserts the 
fact that "Alfred the Great was a scholar," and when asked 
for proof says, "Because he founded the University of Oxford." 
Now, there may be distinct proofs that he was a scholar, but 
13 K 



146 LOGIC. 

this certainly is not conclusive. Let us state the syllo- 
gism : 

Those who found universities are patrons of learning ; 

Alfred the Great founded the University of Oxford ; 

Therefore he was a scholar. 

The conclusion is irrelevant ; the true conolusion being, from 
these premisses, that 

He was a patron of learning. 

If polemical writings, and especially those which partake 
of the nature of popular and heated controversy, be analyzed, 
this will be found to be the standing fallacy, as often self- 
deceiving as deceiving others, and responsible for much of the 
widespread error in speculative science. 

So varied is its nature that it has been from the early times 
known under various names and presents its insidious temp- 
tations to all kinds of persons. 

Perhaps that form which is of most universal application 
is the argumentum ad hominem, the unfair appeal to personal 
opinions, or to one's vanity or prejudice. After exhausting all 
the arts to prove a thing wrong which is not so, the argument 
closes with " Well, you would not do so !" Even in matters 
of religion we are triumphed over by the adversary by a refer- 
ence to ourselves and our own imperfect actions, when the 
question concerns the abstract truths of God's holy law. This 
form of the fallacy needs, then, a special watch as the most 
insidious. 

Next in enumeration is the argumentum ad populum, which 
is the former fallacy extended from one individual to many, 
from personal opinion to popular prejudice. 

Unprincipled demagogues use this fallacy continually ; and 
where the sophistry would be apparent to any single mind 
gifted with common sense, the enthusiasm and thoughtless 
spirit of a mob, moved by a fiery harangue, is blind to its 
unreasonableness. This may be called the logic of revolu- 
tions. 



MATERIAL, OR INFORMAL FALLACIES. 147 

A third .kind of irrelevant conclusion is the argumentum ad 
verecundiam, or appeal to the modesty or sense of shame of our 
opponent, hoping that he will not presume to attach respected 
authorities and time-honored customs. It is based upon the 
general principle that natural prejudice is in favor of the 
existing and the old. Although healthful progress may 
have demonstrated their errors and provided us with better 
methods, the cry is of recreancy to our fathers' memories, to 
old associations, to History; and thus the world has been 
trammeled and clogged by what professes to be the genius 
of conservatism, but what is in reality the genius of obstinate 
error. 

The argumentum ad superstitionem is an appeal to one's 
superstition, from which, in some form or other, few men are 
free; ad odium is to one's hatred; ad invidentiam, to envy; 
ad amicitiam, to friendship. Many others might be formed 
following this analogy. Those mentioned are sufficient to 
illustrate the principle. 

Besides these forms of irrelevant conclusion, there are many 
which have been proposed in pleasantry, such as the argu- 
mentum ad baculinum, and others which Sterne humorously 
refers to in " Tristram Shandy." 

There are, how r ever, it must be particularly observed, many 
cases in which many of these arguments are not fallacies — in 
which, indeed, they may with great propriety be used, clothed 
with all the graces of rhetoric and imbued with all the spirit 
of enthusiasm. 

The argumentum ad hominem is not a fallacy when the 
design is to teach pure truth, and when no unholy passion or 
emotion of man is appealed to. In this application it was 
used by our Saviour himself to the Jews on many occasions 
with great force and beauty. His touching and yet searching 
appeal to them for the woman taken in adultery sent them 
out one by one before its power. Each one felt the argument 
and admitted the conclusion. 



148 LOGIC. 

His arguments in favor of healing on the Sabbath, and search- 
ing the Scrip>tures, that they might find every page luminous 
with Him whom they denied, were examples of the unfalla 
cious and powerful use of this form of reasoning. 

So, too, an appeal (ad populum), not to the prejudices, but 
to the couscientious scruples and feelings, of a multitude, is 
without fallacy, and is productive of the best results. 

Many customs, long honored and dear to every heart — 
customs national, civic, professional, domestic — unmingled 
with error, unopposed to progress, make the argumentum ad 
verecundiam a most proper and effective appeal. 

But such is the waywardness of man that the temptation to 
fallacy in their use is exceedingly stroug, and must be care- 
fully guarded. 

Argumentum Ad Rem and Ad Judicium. 

Opposed to all these, when used as fallacies, are two forms 
of valid argument : the first expresses a concentration solely 
upon the reason of the thing itself, and is therefore called the 
argumentum ad rem ; the second is when the appeal is made to 
the unbiased exercise of the individual judgment ; this argu- 
ment is called argumentum ad judicium. Many writers have 
increased the number of these fallacious argumenta to a much 
greater extent ; but those given are the principal ones, and 
will sufficiently indicate the process by which they are coined 
when needed. 

Changing the point in dispute. 

Another form of the "irrelevant conclusion" is the fallacy 
of changing the point in dispute, in which one of the parties 
in a long and difficult controversy, after having tried in vain 
to establish his irrelevant conclusion, dextrously shifts his 
ground from the point in dispute to some other, and perti- 
naciously claims that to be true which has not been disputed, 
while the true matter of contention is left without an honest 
confession of his inability to prove his assertion. For ex- 



MATERIAL, OR INFORMAL FALLACIES. 149 

ample, a person undertakes to prove that the people in general 
are not educated: i. e., lie first denies that they are; but failing 
of this, he really proves, what no one denies, viz. : that all 
the people should be educated. 

Fallacy of Objections. 

It has been remarked that Ignorance may state in a few 
words objections against Science which wise men could not 
refute in whole volumes. The truth of this is manifest. The 
error of reasoning from the statement or existence of these 
objections to the falsity of the science is one of the forms of 
irrelevant conclusion which has been called the Fallacy of 
Objections. It consists in asserting that, since there are objec- 
tions against a Science, that Science is false ; whereas the judg- 
ment demands that the claims of the Science as well as the 
objections be duly stated, and that the turning of the scale 
decide whether truth or error predominate. If it be a com- 
plicated system, it will be found to contain portions of both ; 
if an abstract theory, it will stand or fall by such a test. 
This fallacy has been industriously aimed by skeptics against 
the mysteries of the Christian faith, but it soon loses its 
point in such an encounter. 

From the consideration of the various species of the fallacy 
of irrelevant conclusion which have been mentioned, and the 
examples given, it will be seen that it is in all its forms the 
standing sophism in houses of legislative convocation' — that it 
is the demon of debate. Few subjects of debate are so ab- 
stract and unit-like but that dull minds will find room to 
wander about, one losing the very poiut in question, another 
concerned about a crowd of details which have little or no 
bearing upon it, a third mistaking the fine and delicate points 
of the. logical argument; some, becoming heated in the con- 
troversy, will lose their temper and reasoning powers together, 
and, overpowered by the truth and Logic of their opponents, 
will have recourse to appeals to the prejudices and interests 

13 * 



150 LOGIC. 

of their audience; and others, more shrewd than just, will 
seek to bring by similar means the cause and persons of their 
adversaries into disrepute by the light arrows of ridicule or 
the more ponderous weapons of insult. It is amidst such 
scenes, and under such circumstances, that the master mind 
shows itself as it rises over the storm of the debate, and brings 
them back first to the consideration of the subject in dispute 
in its true and abstract form. Perhaps the most striking 
illustration of this is found in our own Congressional history. 
After Mr. Webster's first speech on "Foote's resolution," 
many senators had delivered their views, and much sectional 
excitement was aroused. Mr. Webster began his famous 
second speech, with just such a master-effort to come back to 
the true merits of the controversy : 

"Mr. President, when the mariner has been tossed for many days 
in thick weather and on an unknown sea, he naturally avails himself 
of the first pause in the storm, the earliest glance of the sun, to take 
his latitude, and ascertain how far the elements have driven him from 
his true course. Let us imitate this prudence, and before we float 
farther on the waves of this debate, refer to the point from which we 
departed, that we may at least be able to conjecture where we now are. 
I ask for the reading of the resolution before the Senate." 

The resolution was read ; the Senate found their true posi- 
tion, and Mr. Webster's speech is as masterly for its logic as 
for its oratory. 

(50.) Verbal Fallacies. 
There is still a most important class of invalid arguments 
to be considered ; it is that growing out of the ambiguous or 
equivocal meanings of words, many words being identically 
the same, and yet bearing widely different meanings. Thus, 
the simple w r ord line, when used in different connections, 
means many distinct things: for example, a cord used in fish- 
ing ; a few words in a letter ; an arrangement of troops or ships 
in battle array ; and when we see the word porter, we are in 



VERBAL FALLACIES. 151 

doubt which of three meanings is intended — a gate or door' 
keeper, a man who bears burdens or a kind of malt drink. 

In most such cases, however, there is a single root to which 
we may trace all these secondary meanings; thus all the 
meanings of a line refer to the mathematical definition that 
it is length, without breadth or thickness, and all the uses of 
porter refer to the Latin word which signifies to bear. 

It is true that there are examples of words spelt alike which 
have different etymologies, but these are few : host from 
hostis, and host from hostia in the sacrifice of the mass, are 
examples of this ; so also league from ligare, to bind, and 
league from the Latin locus or distance between places, con- 
tracted in French to lieue, as the word focus is into feu, are 
examples of such words. With these few illustrations of am- 
biguous terms, let us see how they are used in argument. 

The ambiguous word is sometimes the middle term and 
sometimes it is the major or minor ; in most cases, however, it 
assumes the former place, so that the general name given to 
this form of verbal fallacy is " the Ambiguous middle." 
X Y 



A bank is the border of a stream. 
Z X 



This stone building is a bank. 
Therefore This stone building is the border of a stream, etc. 

Now, if this glaring and absurd fallacy be stated by sym- 
bols, we shall have — 

X is Y, 
Z isX, 
Z is Y, 

which is the form of a valid argument in the first figure ; so 
that the fault lies in the matter of the propositions which 
compose the argument, and not in the form, which is correct ; 
the fallacy then must be classed, with such an investigation, 
among the material and not among the formal fallacies. But 






152 LOGIC. 

let us go a step farther ; since " a bank" in the major premiss 
means something entirely different from "a bank" in the 
minor, they are in reality different terms; let us symbolize 
them by different letters, and calling the first X, let us call 
the second P ; we shall have, writing by symbols, as before, 

XisY, 
Z isP, 
Z is Y, 

a formal fallacy, in which there are, contrary to the rules laid 
down, four terms instead of three ; and this comes within the 
province of Logic. The fallacy of Ambiguous middle has 
very justly, then, been called by logicians a semi-logical fal- 
lacy ; before we discern the ambiguity it is a material fallacy, 
with which Logic is not concerned ; but as soon as we discover 
the ambiguity, it discloses four terms which make it a- formal 
or logical fallacy. It is because of this peculiarity, and be- 
cause it is so very much used in common life, that we treat 
of it under the distinct head of verbal fallacies. But we have 
said that it is not only in the middle term that this ambiguity 
occurs ; it also happens in the major and minor terms, and is 
quite as sophistic when it lurks there as in the middle term. 
We have therefore discarded the title " Ambiguous middle," 
as applied to the general class, preferring "Verbal falla- 
cies," as more truly illustrative of the error in any of the 
terms. 

There are many ways in which words come to be used 
ambiguously, and we shall give a few of them, with illustra- 
tions ; and first we place the influence of Etymology. 

I. Etymology. 

A word which originally meant one thing now means quite 

another, and the fallacy consists in 'using it in the two senses, 

in two propositions of the syllogism. Thus, taking the first 

meaning of pagan to be a villager (paganus*), and its present 

* From pagus, a village. 



VEKBAL FALLACIES. 153 

meaning to be a believer in some other religion than that of 
Christ, we have — 

A pagan is a disbeliever in Christ ; 

Every villager is a pagan; 

Every villager is a disbeliever in Christ. 

Akin to this, and indeed ranging under the general subject 
of etymology, is the use of paronyms, or paronymous words. 

Paronymous words are the noun substantive, adjective, 
verb, etc., belonging to each other and springing from the 
same root. To project, project, projection, projector, etc. are 
paronyms, springing from the Latin compound of pro and 
jaceo. So presume (in its two senses), presumption, presumptive, 
presumptuous, etc. are paronyms growing from the root presumo. 

Take the following example, in which the ambiguity will 
lie in the middle term : 

Presumption is impertinence ; 

That the sun shines, I presume (or, is my presumption) ; 

Therefore I am impertinent (in asserting that the sun shines). 

It will be remembered that the true logical form of the 
minor premiss, which is usually written, " I presume that the 
aun shines," is — 

subj. pred. 



That the sun shines is presumed by me. 
Again : 

To propose a railroad is a project (or a projector's work). 
This man proposed a railroad. 
Therefore He is a, projector (or visionary man). 

In which the ambiguity lies in the major term. Now, no 
one can work advisedly without making projects, whereas 
one of the meanings of projector is a scheming and visionary 
man who ought not to be relied upon. 

II. Fallacy of Interrogations. 
This is a use of two or more terms in a question, making 
thus in reality two questions, requiring two distinct answers, 



154 LOGIC. 

and the ambiguity lies in the single answer given to both. 
It is common for those who use this fallacy to express but 
one question, while the other is implied. Thus, if a man 
who has always been temperate is asked, " When he gave up 
drinking f" the implied question is, " Did he ever drink t" and 
then, if so, when did he cease f or, in the celebrated inquiry 
of King Charles II., "Why a live fish does not add to the 
weight of a vessel of water f" the implied question being " Does 
a live fish add?" etc., and if so, "why?" etc., or a witness 
may be asked, Where were you when the prisoner murdered 
the deceased ? which would imply what remains to be proved, 
viz., that he did murder him. This fallacy, which is called 
by the writers Fallaeia plurimum interrogationum, is made 
more subtle by the number and closeness of resemblance 
of the points included in the questions. 

III. Amphibolous Sentences. 

Sometimes the ambiguity, instead of residing in the words 
which compose the argument, lies in the construction, and 
thus, by different punctuations, we have double and opposite 
meanings. This passes from the ambiguous words to amphibo- 
lous sentences. Among the most celebrated of these is the 
response of the Delphic oracle to Pyrrhus when he went to 
encounter the Romans : 

Aio te iEacida Komanos vincere posse, 
Ibis redibis nunquam in bello peribis. 

In the first line, either accusative may be taken with the 
iufinitive, thus making either " Pyrrhus " or " the Romans " 
able to conquer; and in the second, nunquam may qualify 
either redibis or peribis. 

So also in the Nicene Creed, we have, in reference to our 
Saviour, the words, " being of one substance with the Father, 
by whom all things were made." 

The latter clause, so manifestly introduced by the Council 



VEKBAL FALLACIES. 155 

to declare the creative power and Godhead of Christ, in reality 
by strict rhetoric applies to " the Father." 

The name given to this fallacy is the fallacy of amphib- 
olous* sentences, i. e., tossed from one to another with a doubt- 
ful meaning. 

Causes of Ambiguity. 

Having mentioned the various kinds of ambiguity in words, 
we come to consider why words have two or more meanings. 

We have already seen that many words expressing simple 
primitive ideas grow by usage to have other meanings, in 
which, however, the primitive idea is to some extent retained ; 
thus, line, in all its meanings, adheres to the mathematical 
notion of extension in length. 

Now, without being able to trace the exact process in all 
cases by which a word is thus gradually changed, we find 
that it ranges itself under one of these heads : 1. Resemblance; 
2. Analogy; 3. Association; 4. Ellipsis; 5. Accident. 

1. Resemblance. Many things bear the same name from 
their actual similarity in appearance. Thus, in carpentry, a 
dove-tailed joint is so called from its similarity to a dove's tail, 
or a spear of grass from its resemblance to the military weapon, 
a spear. So in the military art a "priest-cap" or "swallow- 
tail " is a redoubt so named from its actual resemblance to 
one of these two things, and a " crow's foot " takes its name 
from the form of a bird's talons. 

2. Analogy. Our ordinary speech is full of the use of this 
figure of speech, and this fact has contributed to the am- 
biguity in many words. As resemblance is a similarity in 
appearance, analogy is a similarity in use, purpose or relation. 
Thus, we speak of the arm of a chair, because it holds the 
relation to the chair which the arm does to the human body; 
and thus an arm-chair is a chair which has arms. 

We speak equally of a sweet food, or a sweet sound, because 

* aft<pi and (3aXku. 



156 LOGIC. 

there is a similarity between the relations of the food to the 
palate and the sound to the ear. So a sour lemon and a sour 
individual create relatively similar effects upon the taste and 
upon the mind. 

Ambiguity of resemblance and of analogy are both pro- 
duced and perpetuated by the use of metaphor and compari- 
son, in our ordinary discourse, and a wayward fancy, express- 
ing itself in the social exaggerations of the day, is robbing 
some of our best words of their true shades of meaning ; for 
example, sweet, lovely, horrid, agony, wretch, are deflected from 
their original meanings entirely. 

An argument from analogy may lead to probability, but is 
fallacious when it claims a certain condition, but it may well 
be used to corroborate and strengthen other arguments as an 
additional likelihood. 

3. Association. By this we mean the connection of parts 
in ' the same structure or institution, or to produce a single 
result. Thus, a door is the opening in the wall or the swing- 
ing shutter that closes it. Faith is belief, and " the Faith " is 
the system of Christianity. Shot is the leaden pellet : a good 
shot is either the person who shoots or the effect of the shot. 

It is by the association of ideas, which, unlike our examples, 
are subtle and difficult to fix and determine, that fallacies 
have grown out of this ambiguity ; and such is the want of 
correctness in the language of the great number of people 
that the tendency to this fallacy of words, expressing asso- 
ciated ideas, is particularly strong and dangerous. 

4. Ellipsis. Another habit into which men naturally fall, 
in trying to avoid the use of many words, and words convey- 
ing thoughts which the mind will readily supply without their 
being expressed, is the use of elliptical language. While in 
most cases this is harmless and even profitable, in some it 
leads to error. Thus, we speak constantly of Scott, Byron, 
etc., when we mean their works or their persons. We use the 
form "to my father's," "at Mrs. Smith's," when we mean the 



VERBAL FALLACIES. 157 

houses or "parties" of these persons, and such ellipsis is 
always understood ; but many persons are deceived in their 
business relations by such ellipsis as the statement of another's 
wealth at so many thousands of dollars, when in reality, 
although it may produce the interest on such a sum, it can- 
not be made available for anything like the amount of the 
principal sum mentioned. 

5. Accident. It seems in certain cases as though a word 
had assumed two meanings in a manner inexplicable and 
accidental. Such, for example, is the word light, which is 
equally opposed to heavy and dark, and which in conduct 
means the opposite of serious or dignified. But even in such 
a case we shall find one idea, however subtle, pervading them 
all, and that is the removal of a covering of some sort ; thus, 
light removes the pall or covering of darkness ; the incumbent 
weight of something heavy; the just restraints of dignity and 
sobriety. In strict truth, then, there is no accidental am- 
biguity, for, although there may be words in the double mean- 
ings of which we can discover no relation to a single idea, 
that relation undoubtedly exists, and by a profound research 
the number of such words would be very much diminished. 

Many words are forced into a double meaning by a populai 
or political use, which may be called accidental, but which in 
reality is designed by one party as an equivoque, or strata- 
gem, in the way of retort upon the other. It was thus with 
the use made of the word Pretender*by the English Jaco- 
bites. When it became treasonable in any way to maintain 
the claims of James Stuart, the son of James II., who was 
called "the Pretender," they toasted him in the well-known 

verses : 

God bless the King ; God bless the Faith's Defender ; 
God bless — no harm in blessing — the Pretender. 
But which is the Pretender ? which the king ? 
God bless us all — that's quite a different thing. 

It is evident that such a use of the word would deceive no 
one ; nor was it indeed so designed, but rather to violate the 

14 



158 LOGIC. 

spirit and yet adhere to the letter of the law. The true 
argument used by the adherents of the new dynasty was — 

Those who aid a pretender to the English throne deserve punish- 
ment. 

James Stuart is a pretender. 

Those who aid James Stuart deserve punishment. 

It must be understood that pretender in both premisses 
has the same meaning — i. e., false claimant 

But there is still another form of ambiguity which leads 
to fallacious arguments ; it is where the ambiguity lies not in 
words, but in the context ; or where our assertion means one 
thing when taken in a general sense, and quite another if 
considered in a special sense. Of these fallacies, arising from 
ambiguity in the context, there are two kinds : 

1. The fallacy of accidents. 

2. The fallacy of division and composition. 

Under the first head are included the Fallacia accidentis, 
and the Fallacia a dido secundum quid ad dictum simpliciter. 
These are the converse of each other. 

Fallacia accidentis. 
This is where, in one premiss, we assert something of a 
subject in a general sense, and, in the other, place upon that 
subject some accidental peculiarity which will lead us to 
error in the conclusion, thus : 

Things bought in market we eat. , 
Raw meat is a thing bought in market. 
Therefore Eaw meat is what we eat. 

Here the middle term is things bought in market, and it is 
considered in the major premiss as to its essence, viz. : that 
these things are in market for general use as food ; in the 
minor we lose sight of its essence, and only regard some acci- 
dent of it, viz. : that the meat bought in market is raw. Thus, 
in reality, the error is thrown upon the middle term, which 
is shown to be not one, but two distinct terms, and the fallacy 
is thus exposed. 



VEEBAL FALLACIES. 159 

The other form of this, which for shortness is called the 
Fallacy of Quid, may be translated reasoning from the re- 
stricted or limited sense of a term (secundum quid — i. e., ali 
quid in the monkish Latin), to its broad or unrestricted use (ad 
dictum simpliciter). Thus : 

This man is innocent (of a certain crime) ; 
But the innocent (entirely) are sure of Heaven ; 
Therefore This man is sure of Heaven. 

Fallacy of Division and Composition. 
In this fallacy the middle term is used in its collective or 
additive sense in one premiss, and in its distributive sense in 
the other. When the middle term is used collectively in the 
major premiss, and distribuiively in the minor, the fallacy is 
of " Division ;" when the reverse takes place, it is a fallacy of 
"Composition." The following are examples: 

Fallacy of Division. 
The Christians (as a sect) were persecuted at Rome. 
Constantine was a Christian (individually). 
Therefore He was persecuted at Borne. 

Fallacy of Composition. 
Three and two are two numbers (distributively). 
Five is three and two (additively). 
Five is two numbers. 

Positive and Negative Intention. 
Akin to these fallacies are those absurd conclusions reached 
by a play upon certain negative words, such as nothing and 
no, when used as an adjective ; thus, 

Nothing is better than Heaven. 
A shilling is better than nothing. 
Therefore A shilling is better than Heaven. 
No cat has two tails. 
Every cat has one tail more than no cat. 
Every cat has three tails. 

In these examples the middle terms nothing and no cat are 
taken in a positive sense in the major premiss, as though they 



160 LOGIC. 

expressed living or existing things, while in reality they mean 
non-existence. In the minor premiss they are taken in their 
true negative sense. 

The best method of refuting them is to deny the major 
premiss, or to demand that it be put in other words, thus : 

It is not true of anything that it is better than Heaven ; 
which will foil the one who wishes to draw the absurd con- 
clusion. It should be observed that such arguments are 
really used only in sport, but it is well to detect and under- 
stand the error which they contain. 

(51.) The Manner of Removing Ambiguity in Terms. 

The true method of ridding ourselves of this ambiguity of 
terms in argument is to demand a definition in each case, and 
to keep our terms distinct when thus denned. It will not, in 
most cases, be necessary to give a real definition, as a nominal 
one will answer every purpose. The ambiguity is usually such 
that by giving the true, limited and exact name (which is the 
province of a nominal definition) we shall detect and remove it. 

In many cases where the fallacies consist of a number of 
arguments and many ambiguous terms, the first thing to be 
done is to disentangle the web of sophistry by writing them 
out in full and in due order, and then, after detecting the 
terms in which the ambiguity lies, to demand a definition in 
a few but plain and conclusive words in every case. 

The equivocal nature of the word becomes apparent if we 
change the language, as in the translation of the familiar 
example into Latin — 

Light is contrary to darkness, 
Feathers are light, 
Therefore Feathers are contrary to darkness, 

we shall have — 

Lux est contraria tenebris. 

Plumse sunt leves. 

Plumse sunt contrarise tenebris.* 

* Latham's Logic, p. 221. 



THE FALLACY OF PROBABILITIES. 161 

This change of language, it will be seen, is of the nature of 
a definition. 

(52.) The Fallacy of Probabilities, or the Calculation 
of Chances. 

This consists in stating two probable premisses, and then 
drawing a certain or more probable conclusion, as though the 
number of probabilities combined amount to certainty, where- 
as, in most cases, the conclusion will be less probable than 
either, thus : 

Those who have the plague probably die ; 
This man probably has the plague ; 
Therefore He will {certainly) die. 

Whereas, suppose ten out of tivelve of those who have the 
plague die, then if we express certainty by the number 1, that 
probability is expressed by the fraction ^-J or -J ; and if it is 
an even chance whether or not he has the plague, that proba- 
bility will be expressed by \. The probability of the conclu- 
sion, therefore, will be f X \ = t%, or as \ is the expression 
for perfect doubt, i. e., an even chance of his living or dying, 
he is less likely to die than to live, his chances of dying being 
5 out of 12, and of living, 7 out of 12. 

This fallacy is practically used in times of sickness and 
mortality, when fears of evil, excited by nervousness, affection, 
etc., place an anticipated conclusion for the true one. 

When, instead of one syllogism or enthymeme, many are 
combined to make a compound argument, and the errors of 
probability are thus multiplied, the result will be at once 
farther from the truth and more difficult to detect. 

Let us deduce then a simple rule for the calculation of 
probabilities. The subject has been called "the doctrine of 
chances." 

When we speak of chance, we really mean probable results 
of God's laws, and in the use of either word we express our 
ignorance of the connection between natural causes and effects, 
14* L 



162 LOGIC. 

Now, as that ignorance may be partial or entire, we are thrown 
upon a calculation of the chances, and we shall find that the 
probability ranges between the two extremes, certainty and 
impossibility. We do not pretend to assert by this that man 
may divine the results of God's doings in the future ; but that, 
according to the action of natural laws and the sequence of 
an established order, we may approximate to the truth with- 
out assuring ourselves of it. 

Thus, in throwing dice, we cannot be sure that any single 
face or combination of faces will appear ; but if, in very many 
throws, some particular face has not appeared, the chances of 
its coming up are stronger and stronger, until they approach 
very near to certainty. It must come ; and as each throw is 
made and it fails to appear, the certainty of its coming draws 
nearer and nearer. 

The probability of a single event depends upon the number 
of chances of which it is one. Thus, if A is in a single action 
where 10 men are killed, his company numbering 50, the 
chance which each man stands of being killed, and conse- 
quently that of A, is -J-g- or -J. If we subtract -J- from 1, or 
certainty, we shall have •§- for his chance of being saved. The 
calculation of probabilities becomes more complicated where 
the events are combined. Thus, if in a second action 10 men 
more are killed, his chance of being killed in this last action 
is as 10 to 40, or \, and that of his being saved f . If now we 
would determine his chance of being saved, after both actions, 
we must multiply the two chances together : f X f = M = 
f , which is as it should be, since 20 men are lost of the orig- 
inal 50 and 30 remain ; his chance of being among the latter 
should be as 30 to 50, or f . 

It is upon this principle of calculating chances that insur- 
ance companies are founded, and it finds a benevolent issue 
and scope particularly in those life-assurance companies which, 
demanding but a small percentage, making a large aggregate, 
are thus enabled to pay to widows and orphans an honorable 



POPULAR FALLACIES. 163 

support, snatching out of the jaws of death the means of life 
and social comfort. 

It is, however, upon a false study, or rather in an ignorant 
and fatal reliance upon this principle, that those who frequent 
gaming-houses throw away their means, reputation and life ; 
for the true gainers are not the frequenters of the gaming- 
table, but the keepers, who are acting upon this very doctrine 
of chances. By a calculation of chances it is found that, in 
the long run, the keeper of a gaming-house must win in almost 
every kind of game played, while only an occasional player, 
with what is called a marvelous run of luck, chances to win 
largely. 

The subject of probabilities, which in its right use is not 
fallacious, but is reduced to arithmetical accuracy, has been 
placed under the general head of Fallacies, because of its 
being so liable to fallacious use, and so much employed thus. 
Mingling as it does with the superstition in our nature, we 
deem those things more probable than they are which we 
desire or fear. 

The wish is father to the thought for pleasant hopes, and 
presentiments of evil are taken for its probable coming in our 
gloomy periods. We give a rule by the use of which all this 
may be avoided. 

Rule. — The probability of any event is expressed by a frac- 
tion of which the numerator is the number of chances in its 
favor, and the denominator is the sum of all the chances ; 
and the probability of any two or more events jointly occur- 
ring will be obtained by multiplying together the fractions 
expressing the probability of each. 

(53.) Popular Fallacies. 

It will be well, before closing the chapter on Fallacies, to 

show their practical use, especially in a popular illustration. 

A community, a state, a nation, will unite upon a fallacy 

from which it will be a sort of social treason to dissent ; an 



164 LOGIC. 

age will be tinctured by error, pervading all classes, which 
only the innovation of a succeeding "age can remove ; a false 
principle will cling to human nature, in the mass, during 
many centuries, which the philosophic mind can only deplore 
in secret. 

It will be our purpose, then, to put forth some of the sim- 
plest forms of popular- fallacy, beginning with the most gene- 
ral. Some of these have been already mentioned in their logi- 
cal places, as the different forms of irrelevant conclusion, etc. 

I. The fallacy which is expressed by the adage, Nil de 
mortuis nisi bonum. There is a j list meaning to this indeed ; 
it is that the tongue of private enmity should be silenced — 
that we should consider Death as having adjusted all difficul- 
ties as between man and man, and awed our mortal infirmi- 
ties into a silence and forgetfulness of the evil which existed 
in him who is now dead. So far the adage is good ; but when 
it becomes a principle in public morals, when it tinctures the 
historian and the historical biographer, who should deal with 
the dead as with living defendants, arraigned for trial, its evil 
nature is apparent. When it eulogizes the dead at the ex- 
pense of the living, and runs riot in obsequious praises and 
flattering epitaphs, it assumes its most sophistic form. "The 
same man," says Jeremy Bentham, "who bepraises you when 
dead would have plagued you without mercy when living.' ' 
The reason of this is apparent. A dead man cannot be a 
rival ; he incurs nobody's envy, and is removed from all the 
results of malice. 

II. Not unlike the preceding is the fallacy conveyed in the 
trite saying, De gustibus non est disputandum. This is used 
fallaciously to put a stop to controversy ; the assertion imply- 
ing that as God gave man each his own taste, one taste is as 
good as another. But all our systems of education teach us 
that this is not true — that there is, on every subject which 
comes under the dictum of taste, a true standard which can 
and ought to be used. It certainly is better to put an end to 



POPULAR FALLACIES. 165 

controversy by saying that it is better to differ than to become 
excited and quarrel, than falsely to state that there can be no 
dispute about tastes. 

III. There is a fallacy which particularly assails patriotism : 
it is the fallacy of asserting that any one form or system of 
government is abstractly the best. The Russian deems that 
men cannot be controlled in masses without single autocratic 
power ; the Englishman defies the world to pick a flaw in his 
limited monarchy and superb aristocracy ; while the Ameri- 
can boldly declares that the best government is the democratic 
representative form. Where such men as Milton and Locke 
have " astonished the world by signal absurdities " in their 
models of government, we might be sure that its theory must 
be difficult ; but the truth is, there is no abstract theory of 
human government. 

Asiatic barbarians, when they leave their patriarchal 
wandering life, as in Russia, and come into the first corrup- 
tions of a half-civilized life, must be governed by despotic power : 
they cannot be republican ; while on the other hand, it is only 
where education is general among the people — that they may 
know their wants, and how to supply them, and where indi- 
vidual honesty and virtue are everywhere felt, that no undue 
means may be taken to bring about such an end — that a 
democratic government is the right one. Then, in this freest 
form there is a reciprocal influence between the government 
and that upon which it is founded. A free government en- 
lightens and purifies the people, while the enlightenment and 
purity of the people strengthen and ensure the government 
under which they live. 

IV. There is a popular fallacy which may be called Sweep- 
ing classifications. It consists in ascribing to an individual 
something really belonging to another individual, only because 
the two happen to be of the same class ; thus, during the 
French Revolution, when the fate of Louis XVI. seemed to 
hang upon a thread, one pamphlet was issued with the title 



166 LOGIC. 

" The Crimes of Kings." Now, as there had been many bad 
kings in Europe and not a few in France, Louis XVI., the 
best of them, was put into the category of condemnation 
simply because he was a king. 

Thus misusing the adage " ah uno disce omnes" govern- 
ments and institutions, both secular and religious, are blamed 
because some of their members indulge in crimes entirely 
their own. The entire body is made to share in the condem- 
nation because the few are guilty. 

V. Space would fail in which to enumerate the current 
and manifest popular fallacies, most of which are used in 
legislatures and councils, and are considered in the light of 
shrewd and dextrous diplomacy. There is the " no precedent 
argument." It is stated thus : " The plan proposed is entirely 
new. This is certainly the first time such an idea has been 
broached in this honorable house; and therefore the secret 
hope is that this house will not now entertain it." 

Next, we have personalities introduced, laudatory or abu- 
sive, by which to turn the current of the argument. 

Another form is the assertion with regard to any measure 
that as " no complaint has ever been brought against it be- 
fore, it must be a good one." 

But perhaps the most insinuating form of popular fallacy 
is that of authority by which a man is required to join one or 
the other party in every question, thus causing the young 
ignorantly and prematurely to commit themselves to views 
and measures which later experience teaches them to be 
wrong ; if then they change they are traitors or turncoats, if 
it be a national or political question, and fickle and unreli- 
able, if it be of a less general nature. It is lamentable to 
see party guides bringing those under their control forward 
to swell the ranks of their party, and those thus introduced 
glorying in their new distinction, when self-interest and not 
truth has been the motive on both sides. 



CHAPTER XI. 

THE FUNDAMENTAL LAWS OF THOUGHT, OB FIRST 
PRINCIPLES OF REASON. 

Having thus explained the various logical processes by 
which the mind seeks to establish truth and detect error, and 
having explained the subject of fallacies in form and in mat- 
ter, the existence and prevalence of which show the necessity 
of an exact system of logic, it will now be proper to lay 
down for students the fundamental laws of thought, or what 
may be called the first 'principles of reason. 

A primary principle is one which has no cause or reason 
behind it upon which it depends. It is recognized as true 
without proof, for it cannot be proved ; it is necessary, uni- 
versal and underivable — that is, it belongs to mind as a neces- 
sary part of its existence, it belongs to all minds, it depends 
on nothing antecedent of itself. 

The number of these first principles has been more or less 
extended by different schools of philosophy, but there are 
four upon which most philosophers are agreed, viz. : Iden- 
tity, CONTRADICTION, EXCLUDED MIDDLE and the law of 

reason and consequent. Upon these as a basis the sys- 
tem of Logic is reared as a superstructure. 

I. Identity. With the belief or cognition of our own 
existence comes the belief that whatever is, is, or, in the lan- 
guage of the older schoolmen, Omne ens est ens. In regard 
to any object the mind at once affirms it of itself, and can- 
not think of it but as existing. The law of identity, it will 
be readily observed, is the principle upon which logical 
affirmative propositions and definitions are formed. Thus, in 

167 



168 LOGIC. 

the proposition All A is B, the identity of the whole of A 
with a part of B is set forth. 

II. Contradiction. Simultaneously with this intuitive 
belief in identity appears the second principle, Contradiction, 
or, in the words of Sir William Hamilton, more properly 
non-contradiction, which has been called the highest of all 
logical laivs, which gives sole value to identity. The law of 
contradiction declares that we cannot conceive of a thing as 
being and not being at the same time. If identity declares 
that A is A, the mind refuses its assent to the contradictory, 
A is not A. Upon the law of contradiction is based all neg- 
ative judgments and logical distinctions. 

III. Excluded Middle. This law asserts that there can 
be no medium between the dictum of identity and that of 
contradiction, or it excludes such a medium. The two propo- 
sitions, A is A and A is not A, being of such contradictory 
nature that if one is true the other must be false and vice 
versa, no medium between them can be conceived. We must 
think of either the one or the other as existing, and they 
cannot co-exist. The law of excluded middle, it will have 
been seen, has been set forth in a disjunctive proposition, 
Either A is A or A is not A. By identity and contradiction 
we conclude that if one contradictory proposition is true the 
other is false. By the action of excluded middle we reason 
from the falsehood of one to the truth of the other. 

IV. Keason and Consequent. The principle here set 
forth has been called also that of sufficient PvEASon. This 
implies that wherever a reason exists there must exist a con- 
sequent, and conversely, wherever we have a consequent, there 
must exist a sufficient reason for it. 

Logic applies this principle directly in the reasoning pro- 
cess, and forms in close and necessary connection the series 
of notions which thought has produced. The axiom of Kea- 
son and Consequent must be kept quite distinct from that of 
Causality, as will be seen. 



THE FUNDAMENTAL LAWS OF THOUGHT. 169 

It is a significant fact that these laws were not developed 
by philosophers in the order .stated. The principle of contra- 
diction was enounced by Plato and emphatically stated by 
Aristotle, while the law of identity was not enounced as a co- 
ordinate principle until long after. Hence there has been a 
controversy among philosophers which of these is the first or 
highest principle ; some assert that our own existence even is 
not a primary datum of intelligence, but is an inference from 
the existence of thoughts and feelings of which we are imme- 
diately conscious. Some would claim Identity to be first in 
order, while others regard Contradiction as the principle by 
which Identity is established, and without which it cannot be. 
So too there have been those who doubted whether contradic- 
tion was really a primary principle, an a priori datum of in- 
telligence, or whether it was not a generalization from our 
earliest experience. With most, the essential fact is identity, 
the essential law, contradiction. Leaving such matters to the 
metaphysician, we may not only agree to consider contradic- 
tion a primary principle, but go farther, and assert that it lies, 
as it were, at the foundation of the others, and is implied in 
them. It is clear; it is universal; it is necessary. 

It is clear, as is shown by the fact that it depends on the 
same evidence as the simple notion of existence, of which it 
is an affirmation, in that whatever is cannot not be. Thus it 
establishes identity. 

' It is universal, because, as the idea of being is implied in 
every apprehension and in every principle, so is this distinct 
affirmation of it applicable to all. 

It is necessary, because by it reason must be guided in all 
its judgments, since through the excluded medium it estab- 
lishes the absolute truth that being and not being cannot sub- 
sist together. 

Let it be observed that we do not say that the other prin- 
ciples may be demonstrated by the principle of contradiction, 
but it holds place as the highest principle only as the others 

15 



170 LOGIC. 

may be resolved into it. Demonstration supposes the thing 
to be demonstrated less evident than the medium quo, that by 
which it is demonstrated. Now, each of these first principles 
has its own intrinsic and immediate value and truth, and can- 
not be demonstrated. 

It further appears that the law of contradiction governs all 
the principles of reason as a motive and guiding power, in- 
fluencing the intellect to give its assent to that which with- 
out it would be incomplete and inert. 

In necessary truth, the intellect affirms the truth of the 
principles which it perceives, because it sees the necessary con- 
nection between the two ideas compared, and at once explains 
or rather satisfies itself of the necessity by the principle of 
contradiction ; or the truth of this principle, as an intuitive, 
undemonstrable truth, is sanctioned by the truth that its 
contradictory cannot be. 

And what is seen in necessary truth is equally manifest in 
contingent truth. Truth is contingent when it depends for 
its existence upon some hypothesis or condition or cause or 
fact. Here the mind discerns that the truth exists because 
the condition exists and not otherwise, and hence by the law 
of contradiction that its contradictory must, on the same con- 
dition, be false. 

Without entering into the speculations of philosophers in 
all ages of history, it seems to us that the principle of contra- 
diction is the foundation and ultimate reason of all proof 
and of all assent of the intellect; that, so to speak, it gives 
vitality to the law of Identity, and suggests the necessity of 
excluded medium, establishing itself as a sufficient reason for 
both. 

These principles are intuitive cognitions or a priori convic- 
tion, perceptions from which we reason ; concerning which we 
cannot. To this extent they are incomprehensible ; we know 
them to be, but not how and why they are. They are called 



THE FUNDAMENTAL LAWS OF THOUGHT. 171 

a priori principles because they are before all our experience 
and before all possibility of proof. 

Upon them are based, with greater or less claim to intui- 
tive judgments, numerous axioms, such as the -whole is greater 
than a part, and a part less than the ivhole. Two things which 
are equal to the same thing are equal to each other. By ex- 
tension of these axioms in Logic, we have also two terms 
which agree with one and the same third, agree with each other ; 
and of two terms, if one agree and the other disagree with the 
same third, they will disagree with each other. 

It will not be without interest to say a few words in this 
connection concerning the question of causality, or, whence 
do we derive our notion of cause and effect? Various solu- 
tions have been proposed, so diverse and conflicting as to be 
in themselves properly named series implexa causarum. It 
seems to lie so near the first efforts of the mind that many 
philosophers have supposed the judgment of causality to be 
an a priori knowledge referable to a special principle of in- 
telligence designed for it, and it alone. Others have variously 
considered it to result from experience, induction, general- 
ization and custom. 

In common language, the phenomenon may be thus stated : 
we cannot think of anything beginning to be without think- 
ing of its having already existed in another form — that is, the 
necessity of our intelligence makes us believe of anythiug 
that it has a cause ; and as the cause by the same process is 
believed to have a cause, the mind of necessity goes back in 
the chain of causes until it reaches the idea of a first cause. 
What is the limit of the mind in this search ? This limit has 
been called The Conditioned, and the law of the conditioned 
is, that all that is conceivable — as, for example, in time and 
space — is bounded or limited by extremes which are incon- 
ceivable and contradictory, one of which must therefore be 
true. Thus we have, as one set of inconceivable extremes, 
absolute commencement and absolute non-commencement, 



172 LOGIC. 

both of which are inconceivable, and yet one of which is true. 
The conditioned is based upon the principle of contradiction, 
and it explains the true theory of causality. Thus the judg- 
ment of causality is a derived judgment, not from the power 
of the mind, but from its impotence to attain to the extreme. 
When an object appears to us as commencing to be, we can- 
not but suppose that what it now contains has existed before 
in some form — that every thing we see is an effect which must 
have had a cause — but why, or, of what, the cause is, we may 
be, and in some cases must be, ignorant. This inability of the 
mind to reach final causes, and thus to complete the explica- 
tion of the principle, is expressed in negative adjectives, in- 
finite, unending, illimitable. 



CHAPTER XII. 

(54.) Of Certain Modes in which Logic is Applied. 

It is not within the scope of this work to enter upon the 
subject of applied Logic: this would require an investigation 
of all the sciences, or at least of a very numerous classifica- 
tion ; but it is designed to explain the meanings of certain 
phrases which refer to the general applications of Logic. 

We- have the phrase moral reasoning, and it is often used 
as if conveying an opposite or contrary meaning to demon- 
strative reasoning. 

This has reference, not, as we have clearly shown, to the 
kind of reasoning, as there is but one, but to the nature of 
the evidence employed, the meaning of evidence being that 
testimony which sets forth the truth of a proposition. Then, 
moral reasoning is the use of evidence in moral subjects, and 
demonstrative reasoning its use in mathematical subjects. 

Now, evidence may be of three kinds — that is, as to the man- 
ner in which we obtain it ; it may be intuitive, inductive or 
deductive. 

Of Intuition, Induction and Deduction. 

We come now to consider the means of discovering truth 
which are most useful, but which have been strangely con- 
founded with Logic. They are processes as much bound by 
logical laws as all other movements of the reason are. 

It is evident that, in order to the logical process, we must 
have premisses; now, these premisses are obtained evidently 
by the three methods just mentioned, intuition, deduction 
and induction or experiment. 

15 * 173 



174 LOGIC. 

By intuition we mean the immediate and absolute know- 
ledge which, without any apparent effort, we find implanted 
in us. Such, for example, is the aspiration of man's soul 
after a Deity, as exemplified in the religious systems of all 
people, even the most barbarous, and such as the existence of 
certain affections and notions of moral conduct. In brief, 
consciousness in most of its forms and the testimony of our 
external senses are said to be sources of intuition. The truth 
of axioms is dependent upon the laws of identity and contra- 
diction. 

But most of our knowledge is derived from what we pos- 
sess already in another form, as where we deduce certain 
inferences from acknowledged premisses or from observation 
and experiment, and generally many observations or experi- 
ments are necessary before we can determine a general law : 
thus, it required centuries of observation to determine the 
Copernican theory of our solar system ; and almost all the 
developments in natural science are the fruit of many obser- 
vations and experiments aggregated in each case to form one 
general law. It is an effort of man by a close study of the 
phenomena (patvofieva) or appearances of nature, to arrive at 
some degree of acquaintance with the noumena {voouf£eva) or 
essences of its objects. 

To unite these was the aim even of the heathen philoso- 
phers, and with their obscure lights they worked ardently in 
the labor ; it remained for a doubter (Sextus Empiricus), two 
centuries after the coming of Christianity, to connect them 
for another purpose, and that was to arrive at a suspension 
of all judgment on objects whose nature is obscure, and thus 
to acquire a certain repose of mind (arapa^ta) and perfect 
equanimity of disposition (jueTftto7va0eta). But the inductions 
of Sextus were never really performed ; he theorized to his 
skepticism, and his theories will not bear the rude hand of 
physical practice. 

In order to illustrate the difference between induction and 



OF CERTAIN MODES IN WHICH LOGIC IS APPLIED. 175 

deduction, let us suppose a law already determined, which we 
state in the proposition A is B. Let any number of particu- 
lar examples, as x, y, z, range under this law, thus, x is A, 
y is A, z is A, and we can manifestly reach the conclusion 
that x, y and z are all and severally B. 

But suppose the general law unknown, and that it be 
approximated to in proportion to the number of particular 
examples ; we shall thus have x is B, y is B, z is B, etc. ; but 
x, y, z, etc., as we increase the number of the examples, rep- 
resent the class A ; hence we may state the law A is B, the 
truth of which will depend upon the number and extent of 
the experiments performed and particular instances observed. 
Or, to recapitulate in syllogistic form : 

Deduction. Induction. 

{Law) A is B. (Part, examples) x, y, z, etc., are B. 

(Part, examples) x, y, z, etc., ai-e A. A is the class to which x, y, z, etc., helong. 

(Conclusion) x, y, z, etc., are B. (Law) A is (likely to be) B. 

Now, there are certain sciences in which, from the nature 
of things, we can never state more certain results from induc- 
tion than this likelihood; but this likelihood, it must be 
observed, becomes greater and greater, and at length touches 
absolute certainty, when we examine many particular in- 
stances and find none of them failing to range itself under the 
law which we call likely, so that at the last we write it to all 
intents and purposes as a categorical proposition, A is E. In 
some sciences we may exhaust all the particular examples 
and finish our induction by a certain law ; or if by induction 
we find any quality or property to belong to the essence of 
the object undergoing the experiment, induction in both cases 
has led, as the other could not, to certainty. 

There are two kinds of induction, material and formal; and 
it is by a want of proper, distinction between them that the 
error has arisen of comparing induction improperly with the 
syllogism, and asserting that while induction is one kind of 
reasoning the syllogism is another — i. e., deduction. 

Hence, Lord Bacon and his followers, finding that deduction 



176 LOGIC. 

generally moved from what was contained in known premisses 
to lower classes or individuals contained in them, threw aside 
the syllogism as useless, and inaugurated induction as the 
new Logic of experimental philosophy. A simple examina- 
tion of material and formal induction will set us right. Ma- 
terial induction is the process of experiment and observation — 
the laborious investigation of facts as to their discovery and 
their combination — but formal induction is obtained by the 
use of the syllogism itself, not confined, as some writers have 
attempted to show, to the third figure, but in most examples 
capable of being at once written out in the first figure, the 
form in which they may be immediately tested by the dictum 
of Aristotle, as in the example : 

Whatever is true of the cow, goat, deer, etc., is likely to 
J' P ' be true of all horned animals ; 

Min. prem. Rumination is true of the cow, the deer, etc. ; 
Concl. (Law). Rumination is likely to be true of all horned animals.. 

The naturalist receives this as the only just conclusion from 
the formal induction to which the syllogism has helped him ; 
but having as yet found no exception to the rule, he writes it 
out boldly and without fear of contradiction, 

All horned animals are ruminant. 

Of certain modes of using Syllogisms. 

Argument a priori. — This is the mode of passing from 
known antecedents to necessary consequents, or, in the sci- 
ences, from cause to effect. Thus, if we consider the being of a 
God and of his attributes to be independently known, as by 
intuition, then we reason a priori to the existence of his works, 
the universality of his providence and the gracious designs 
of his redemption ; this reasoning is most plainly stated in 
the form of the constructive conditional syllogism, the affir- 
mation of the antecedent, or cause, helping us to the affirma- 
tion of the consequent, or effect. 

Argument a posteriori. — This is reasoning from effect to 



OF CERTAIN MODES IN WHICH LOGIC IS APPLIED. 177 

cause. If, by an inverse process, we first study natural re- 
ligion, and experiment upon the wonders of the human mind, 
and then pass back from these. works around us to the estab- 
lishment of the existence of a first great cause who must have 
made them all, we are said to reason a posteriori, or from re- 
sults to their causes. 

Of the two modes of reasoning, both are useful and effect- 
ive, but the reasoning a priori is the most explicit, stating at 
once the cause and reason of the effect and conclusion, whilst 
that a posteriori, though equally conclusive, is not so explicit, 
because it simply proves that the conclusion must be true, 
although not stating its intrinsic cause. Thus, we prove the 
existence of a first great cause from his works, or a posteriori, 
since he is self-existent and therefore has no cause, and con- 
sequently his existence cannot be proven a priori. 

History uses both forms, and combines them with great 
success. Taking, for example, on the one hand, the early ele- 
ments of a nation's life — its people, its geography, its tenden- 
cies of government — history seeks to trace these to their legit- 
imate results among the changing scenes of national ex- 
istence ; while on the other, looking around at the present 
condition and conduct of a nation, she takes these results, and 
tracing them back, in careful combination, with each step re- 
moved from the present, she seeks for their early and prime 
causes in the classic times of the country's origin. 

Argument a fortiori. — This is a method by which we estab- 
lish a stronger conclusion even than ordinary premisses need 
to warrant us. Thus : 

A is greater than B. 
B is greater than C. 
A is greater than C. 

That this conclusion is just there can be no doubt, and that 
the form of it is not exactly that of the regular syllogism is 
equally apparent. 

M 



178 LOGIC. 

To apply the doctrine, let us present the argument by geo- 
metrical notation, and we shall have — 




in which we have the relative greatness of A, B and C. 

But we are entitled, it is evident, to put this in the syllo- 
gistic form : 

Bis A, 

CisB, 

Therefore, d, fortiori, C is A, 

which is Barbara ; or ordinarily Barbara is itself the argu- 
ment a, fortiori, and is only otherwise when A, B and C, in- 
stead of being unequal, are exactly coincident. 

In this latter case, w T e have the old case of convertible terms 
in each proposition, which is not set forth in separate form by 
the Aristotelian Logic. 

This reasoning a fortiori is very effective and proper, and 
was used by our Saviour in his invectives upon Chorazin, 
Bethsaida and Capernaum with thrilling effect. So also is 
it forcibly used by the apostle to the Hebrews (x. 28) in the 
words : " He who despised Moses' law, died without mercy 
under two or three witnesses : of how much sorer punishment 
shall he be thought worthy, who hath trodden under foot the 
Son of God," etc. 

The Investigation and Discovery of Truth. 

We shall now briefly notice the forms of method used in 
investigating and discovering truth, to which at every step 
the canons of Logic may be applied. 

Man has an inherent desire to find truth, and the universe 
around and within, the realms of nature and the domain of 



THE INVESTIGATION AND DISCOVERY OF TRUTH. 179 

mind call that desire into constant activity. This curiosity, 
which " grows by what it feeds on," leads at once to the dis- 
covery of truth, and through the process to the education 
and development of his faculties. 

The methods and order of investigation are : 1. Observa- 
tion ; 2. Supposition or hypothesis ; 3. Induction ; 4. The- 
ory ; 5. Fixed law or fact. 

I. Observation is applied in general to whatever is pre- 
sented by the senses ; by it man discerns at once objects and 
facts. It includes a thoughtful, attentive outlook upon crea- 
tion and a determination by the senses of the marked dis- 
tinctions between existing things, and leads to the next step 
in the order of inquiry. 

II. Hypothesis or supposition. Because certain things or 
conditions exist, we suppose the existence of causes which 
produced them, or of certain determinate effects Avhich spring 
from them. The words hypothesis (Greek, b-ondrpai) and 
supposition (Latin, sub and pono) have the same meaning — 
an underlying basis upon which to build. A hypothesis 
assigns a probable cause or a reasonable connection. It is 
indeed a gratuitous assumption, but it has been so subjected 
to metaphysical conditions that it may be correctly and prof- 
itably used in our process of investigation. A just hypothe- 
sis is one which explains many phenomena and contradicts 
none, and it is a necessary condition that it should do so 
when no other hypothesis can. Thus it establishes a pre- 
sumption in favor of our law or conclusion which must stand 
or fall by the next step in the process, Induction. Hypothe- 
sis is often incorrectly confounded with theory. 

III. Induction is systematic experiment, based upon 
hypothesis. Having made a nidus for our observations and 
experiments, we test it by phenomena ; if they agree with or 
range themselves under the hypothesis, we approach a general 
law ; or if not, we see that the hypothesis is wrong, and 
assume a new one. 



180 LOGIC. 

IV. Theory is the probable establishment of our hypothe- 
sis through the medium of Induction. In proportion as our 
experiments conform to the hypothesis it becomes probably 
true; as the experiments increase in number and still con- 
form the probability approaches certainty, until at length 
we either reach certainty or, satisfied by sufficient induc- 
tion, assume it, and arrive at a fixed law or fact. 

It will be obvious that these forms of method, although 
distinct, really run into each other more or less as we pro- 
ceed ; that in preliminary observation we may use the sim- 
pler modes of induction ; that in hypothesis we are antici- 
pating theory, and hoping that we have probably assumed a 
law which shall be arrived at. But in systematic investiga- 
tion they are mainly used in this order. Thus, Franklin 
observed the similarity between the spark from an electrical 
machine and a flash of lightning ; he supposed or assumed 
as a hypothesis that they were the same ; he experimented by 
flying his kite and leading the lightning along its string, and 
he then stated his theory of electricity, which, covering all 
phenomena and contradicting none, has assumed the charac- 
ter of an established law. 

Of the Nature and Kinds of Evidence. 

As the investigation of truth, according to the methods 
just stated, depends on evidence, we shall merely state the 
nature and kinds of evidence by which truth is established. 
Evidence (e and video) is that which makes a fact or propo- 
sition clear and obvious to the mental vision. 

Consciousness, the knowledge of the existence of the think- 
ing subject, comprehends all its phenomena ; intuition is the 
act of the mind by which it looks at and into itself; through 
it we have a belief in our own existence, faith in the testi- 
mony of our senses, a reliance upon the uniformity of Na- 
ture's laws. 

Sensation is the effect produced upon our senses by contact 



EVIDENCE. 181 

with the world around us. Sensation does not separate the 
object producing it from ourselves. Perception is the im- 
pression made by an object upon the mind through sensation. 
Through perception we gain the idea of outness or external- 
ity, and thus detach the object from ourselves. These are 
the conditions necessary to evidence, and to these must be 
added memory in its most extensive meaning, as the conserva- 
tive, the reproductive and the representative faculty of the 
mind through which these conditions are made available. 

Analogy is that resemblance between circumstances, rela- 
tions or effects of two objects by which the mind is led to 
accept what is true of one as true of the other ; as evidence 
it is by no means sure, but often corroborative, where other 
evidence is produced. Induction, or systematic experiment, 
is valuable as evidence; in the words of Bacon, "Prudent 
questioning is half the science." 

And last we have the Testimony of mankind, which is 
based upon our natural inclination to believe in the expe- 
rience and truth of others. It is evident that Testimony 
will depend for its value upon the capacity, the character, 
the prejudices, the means of knowing and the number of the 
witnesses. 

An individual of average mind has the capacity to under- 
stand the moral and physical circumstances by which he is 
surrounded. The natural desire of man is to speak the truth, 
and all men unite in despising a liar ; and while on a given 
subject one man may have only partial knowledge, many 
who are cognizant of it, by bringing each his own partial 
knowledge, will present fuller and more trustworthy testi- 
mony than any one by himself. Where fact is in question, 
the truth may thus be readily obtained ; for the chief requisite 
is honesty : where opinion is desired, we must add superior 
knowledge and aptitude which will give authority. 
16 



CHAPTER XIII. 

A HISTORICAL SKETCH OF LOGIC. 

(55.) Division of the Subject. 

Having completed, in general outline, the study of the 
formal Logic, in its present condition of exactness and prac- 
tical use, we are ready to go back to its feeble beginnings, 
and trace it in its slow and trammeled movements from the 
days of the early Greek Philosophy, through the applications 
of Roman Science, the enlightening' process of Christianity, 
the era of the scholastic subtleties, the dawn and advance of 
Experimental philosophy and the metaphysics of the eigh- 
teenth century, down to the controversies of our own day. 

Nor are we yet to regard the science of Logic as estab- 
lished beyond dispute, and fairly stationed among its sister 
sciences ; it is yet an arena of dispute, and the most distin- 
guished philosophers disagree, as has been seen, even as to 
what it is and as to what is its scope. 

It would be of great interest and profit to take such a his- 
torical view in detail,- but the limits of this work will not 
permit it, and, besides, for all practical purposes, the periods 
of the history naturally divide themselves into four. These 
so much transcend all others in interest and value, and so 
absorb the events which just precede or immediately follow 
them respectively, that they form the plainest and most con- 
venient method in which to present the history of Logic. 
They may be marked by the titles — 

1. Aristotle. 

2. Christianity and Logic. 

3. Bacon, and the rise of Inductive Science. 

4. The present system. 

182 






DIVISION OF THE SUBJECT. 183 

1. Under the first may be classed all the efforts of the. 
human mind in the arrangement of a canon of reasoning, in 
that early time when knowledge, preceding method, was only 
seeking in darkness and obscurity that system of laws and 
principles by which alone knowledge may be made available. 
Around Aristotle, too, cluster the great expansions of science 
which were due to the conquests of Alexander and the great 
kingdoms of his successors. 

2. In the coming of Christianity, Logic found, not a rival, 
but a guide, and in the early Church it was the weapon of 
their spiritual warfare. To the Church, as the representative 
of Christianity, is due much of the good of scholasticism. 

3. Logic was the servant, the ill-used servant, of Inductive 
philosophy, and owes much of its long bondage and oppres- 
sion to the illustrious founder of the system of Experimental 
philosophy. 

From these considerations it has been assumed that we are 
better able to look into this history now that we are acquainted 
with the scope of the science ; otherwise, we might fall into 
the same error, by reason of the honorable company in which 
we should find ourselves. 

4. Since the time of Lord Bacon, and perhaps by reason 
of his example in condemning the syllogism, Logic has been 
degraded from its position as the controller of the reason on 
all subjects, and has been so intermixed with Mental phil- 
osophy as quite to lose its identity and be miscalled by its 
own name. This was its condition during the eighteenth cen- 
tury. In the nineteenth there have sprung up many cham- 
pions of Aristotle and the syllogism, among whom first in 
distinction is Archbishop Whately. The universal principle 
of reasoning has been rescued by him from oblivion and deg- 
radation, and Logical science, although still maligned and 
fiercely attacked, seems ready to take its permanent place 
among the great elementary sciences of human investigation 
and instruction. 



184 LOGIC. 

(56.) Aristotle. 

It must be considered that the progress of such a science 
as Logic was necessarily gradual and slow ; that from the 
beginning men had been contemplating the operations of the 
reason, or were making vain but progressive efforts to dis- 
tinguish the exact functions of the reason, among the hazy 
elements of the human intellect. Many men had collected 
much material which lay floating in a chaotic state upon the 
great deep of the human mind. 

The logical doctrines of conception as expressed in terms, 
of judgments as formed in propositions, were known to Socrates 
and Plato. Indeed, Zeno the Eleatic, who is mentioned as 
the inventor of Dialectic, had invented logical puzzles which 
required an investigation of the laws of thought, and that 
caused a race of so-called teachers of Dialectic to spring up 
in Greece. 

So the first movements in Logic were trammeled by the 
ignorance and empiricism of those who called themselves 
teachers. 

The experience of our own age has taught us that true 
science is more impeded and injured in this than in any other 
way. A whole class of speculative logicians in the early 
times went by the name of Sophists. 

We are accustomed to hear the Sophists spoken of in terms 
of contempt, and sophistry has come to mean Fallacy. But 
we should err greatly, as many in all ages have erred, if we 
regarded them as wholly evil. The most enlightened writers 
of modern times have demonstrated that much of the odium 
which attaches to the name belongs really to the abuse of 
their art ; they were paid teachers — among whom are enu- 
merated Protagoras and Gorgias — whose duty was to train up 
young men for the duties and pursuits of public life. The 
character of the Greeks, who were fond of riddles and dis- 
putes, and the errors of the age, led to their real sophistry, 
and their abuse of the rhetorical art to make " the worse ap- 



ARISTOTLE. 185 

pear the better reason ;" after that, their efforts were not for 
the purpose of widening the range of knowledge and truth, 
but really served to check these, and thus give a free course 
to fallacious reasoning. 

The Logic of Euclid consisted in negative proofs ; his de- 
sign was, in encountering an opponent in controversy, not to 
attack his premisses, but his conclusion. 

Chief among the early logicians, as he is distinguished 
among the sages of the world, was Socrates. 

Much interest and sympathy attach to the virtuous and 
heroic life and the tragical fate of this wise and good man ; 
but it is principally by his philosophy and logic that he has 
been useful to the world. Keeping in view always before his 
numerous scholars the dignity of Logic as a science, and the 
loftiness of the reasoning powers, he guided the logical pro- 
cesses by what is now called "common sense." "This is im- 
plied in Cicero's declaration that Socrates brought philoso- 
phy from heaven to earth. Xenophon, likewise, tells us in 
his ' Memorabilia' that when he wished to form a decision on 
any subject, his reasonings always proceeded from proposi- 
tions generally assented to or understood." * Condemning 
the errors into which the Sophists had been led, he claimed 
Truth as the real aim of reasoning, and established in all his 
arguments a high principle of moral responsibility. The 
analytic process was that mainly employed by Socrates ; and 
thus, when Plato appeared, he found the science of Logic 
and the art of Dialectics presented by detached and isolated 
views as the result of previous investigations. The analysis 
had only prepared for the synthesis. 

The plan adopted by Plato was the Synthetic method, and 
by this he worked out many great results. 

Perhaps the best feature in the Logic of Plato was that, on 
approaching the science, he tells us to keep the mind free 
from all preoccupations and preconceptions : he declared, as 

* Blakey's Historical Sketch of Logic, p. 24. 
16* 



186 LOGIC. 

an axiom, that " Ignorance is the true start-point for Science.' 5 
Disputing the assertion of the earlier philosophers that sensa- 
tion was the foundation of truth, he proved it to be one of the 
instruments by which truth is arrived at. Without stopping 
to give a sketch of his system, we may state that his Logic 
and theology are so intimately connected that we may judge 
of the vigor of the one by the developments of the other. He 
proved the existence of a Deity who was the measure of all 
knowledge, the centre of all truth; and in mysterious lan- 
guage he declares that this centre is " the beginning, middle 
and end of all things." But Plato was to be eclipsed by a 
greater mind — in fact, one of the greatest minds the world 
has ever seen. 

Wh^n much material was thus collected, when many vague 
theories had thus been started, and when crowds of ignorant 
pretenders had arisen to be converted or silenced, Aristotle 
came to create a new system — to enlighten, to harmonize and 
to sweep away all the errors of the Dialecticians and the 
Sophists. He who was to correct the characteristic errors of 
the Greek philosophy was himself a Greek. • The Greek mind 
was eminently a curious one. All the speculations of philoso- 
phy, all the systems of Ethics, were directed apparently and 
nominally indeed to the discovery of truth ; but if they 
reached, by specious arguments, a pleasant conclusion, it 
mattered little for pure truth. They contented themselves 
with the fruits of their system, once that system was estab- 
lished. 

The Athenians were characterized by the apostle as " spend- 
ing their time in nothing else" but the pursuit of novelty, 
and they were but the types and representatives of the other 
states and cities of Greece. There are in the early Greek 
authors many corroborations of the apostle's assertion. 

Aristotle, building upon the combined foundations of 
Socrates and Plato, discovered many new principles and 
established new rules, until he had elaborated the system of 



AIHSTOTLE. 187 

Logic which we have at this day. His logical works, pub- 
lished in full under the title of "Aristotle Organon," com- 
prise the following works : 1. The Book of the Categories ; 
2. Of Interpretation ; 3. The Prior Analytics ; 4. The Post 
Analytics ; 5. Topics ; 6. Of Sophisms. 

Of these the most important are " The Book of the Cate- 
gories" and both "Analytics." We shall proceed directly 
to explain their meaning. 

He drew the true and somewhat nice distinction between 
Logic and Phetoric, and established the fact (a fact not yet 
learned by many who call themselves logicians) that Logic 
is not concerned with the truth of propositions, but only with 
the reasoning upon such propositions as are given into its 
charge. If the premisses be true, then Logic will give a true 
conclusion, but if the premisses be false, Logic gives a false 
conclusion ; but in this latter case the Logic is as good, the 
argument as valid, as in the former. 

In establishing his dictum, which we have assumed to be 
the universal principle of reasoning, he laid down the general 
law of Logic — a law which has been misunderstood and mis- 
interpreted, for this dictum was not a model of common 
arguments, but simply a test for all. 

As the Greeks looked for truth and found that Logic did 
not impart it, that before Logic could be used they must be 
possessed of premisses, w T hich premisses are given them either 
by intuition, by deduction or by observation — i. e., induction — 
they either abused Logic for not doing what it could not pro- 
pose to do, or else injured it much more than their abuse 
could do by using it as a vehicle for false philosophy and 
mythic religion. They took, to save themselves the trouble 
of laborious induction in search of premisses, the vagaries 
of their own quick, joyous and disputatious minds, and thus 
produced monstrous and absurd conclusions which, since 
their Logic was valid, they felt satisfied to consider as true. 

The union of this Grecian spirit with the equally vague 



188 LOGIC. 

and fantastic imagination of the Orientals, with whom by- 
conquest they became acquainted, further corrupted their 
intellects, and robbed Logic of its true character and mis- 
sion, leaving the whole domain of Philosophy without the 
true guide of Reasoning. 

Let us now look in turn at the logical works comprising 
the Organon. 

The Categories. 

We are in the habit of using the word category : for exam- 
ple, we speak of a person or thing being put in this or that 
category ; the word and its use we owe to Aristotle. His cate- 
gories are ten in number. They are not all now considered 
of importance in classification, but are still worth an expla- 
nation as the original system from which, by careful elimi- 
nation, we have produced our own later classifications. The 
categories were supposed to imply answers to all possible 
questions concerning a term expressing an act of apprehen- 
sion — i. e., all of which we can have any knowledge. - 

1st, Substance ; 2d, Quantity ; 3d, Quality ; 4th, Relation ; 
5th, Action; 6th, Passion; 7th, The Where ; 8th, The When; 
9th, Position, in space ; 10th, Possession. 

The categories may be thus more fully explained : 

1. Substance may be defined that which is in itself, which 
may be conceived as existing by itself. This is divided into 
spiritual and corporeal, and subdivided according to classes, 
genera, species, etc. 

2. Quantity may be translated how much or how great, 
and by implication, as to time, how long. Thus, under the 
head of Quantity, we have the three special considerations 
of Number, Magnitude and Time (as to duration). Number, 
we know, is either abstract or concrete, as when we speak of 
a number disconnected with any objects, or of a number of 
objects and things. Thus, quantity, as a category, covers the 
science of arithmetic. Magnitude is either linear, superficial 



ARISTOTLE. 189 

or solid; and thus its genus quantity covers, likewise, the 
science of geometry. Time is either permanent or successive, 
and is used to indicate the movements or conjunctions of 
Number and Magnitude. 

3. Quality describes the kind or sort of which a thing 
is, and is subdivided into Habit, or a quality induced by fre- 
quent repetition of the same act, as virtue, vice, etc. ; Inherent 
nature, as man's reason. From these grow the many subdi- 
visions of color, sound, hardness and shape. 

4. Relation is the consideration of two or more objects 
with reference to each other. The first object of two is called 
the relative, the second the correlative, as prince and subject, 
master and servant. 

5. Action has a double meaning ; it is at once the exer- 
tion of power by one body on another and the effect pro- 
duced by such an exertion. 

6. Passion is the endurance of another's action. 

7. The Where includes the three meanings which we 
express by the words where, whence and whither, as in Phila- 
delphia, from New York, to London. 

8. The When has reference to the exact period of time, 
and not its duration, which, as we have seen, belongs more 
properly to quantity. The When may be expressed by the 
phrases to-day, to-morrow, a hundred years ago. 

9. Position has reference, not to the place where, but to the 
posture in which, a body is found, as lying down, standing up, 
kneeling, etc. The question then is, how did you find it? not 
where f 

10. Possession has reference to something belonging to 
the object, or placed upon and clothing it, and as a category 
covers all questions concerning the rights of property. 

Of these categories it will appear that substance stands 
apart from the rest in that it is sensibly existent and they 
are all attributes of such an existence. It will further appear, 
upon examination, that Quantity and Quality are essential at- 



190 



LOGIC. 



tributes, i. <?., belong to the essence of the object necessarily ; 
while Relation, Action, Passion, The Where, The When, Position 
and Possession, are accidental circumstances which may be 
dissociated from it. 

To render this clearer for facility of reference, we state it 
in a tabular form. In this table we place all the explanatory 
parts as by the rules of division before given, but number the 
categories that the eye may at once rest upon them. 

The object or existence expressed by a term. 



Attributes belonging 
to the substance. 



1. Substance. 



Circumstantial. 

I 
4. Eelation. 



Essential. 



2. Quantity 



Number. Magnitude. 



1 

Time. 



3. Quality. 



Habit. 



Inherent nature. 



Shape, etc. 



5. Action. 



Passion. 7. The Where. 8. The When. 



Position. 10. Possession. 



Aristotle asserted that everything which could be said of 
any subject is included in one, some or all of these categories, 
and his own illustration of their use is one of the simplest 
which can be found. It was as follows: " Substance, man ; 
Quantity, one ; Quality, white ; Relation, greater ; The Where, 
in the Forum; The When, yesterday ; Position, sitting ; Action, 
whatever he may be doing ; Passion, whatever may be being done 
to him." 

It is under this first attempt at method that the sciences 
began to range themselves in classes, and by this all other 
systems of classification seem to have been suggested. Thus, 
Substance is the foundation of all Physical and Historical in- 
vestigation ; Quantity, the subject of Mathematics ; Quality, 
of Medicine ; Relation, of Ethics ; Action and Quantity, of 



ARISTOTLE. 191 

Astronomy, Music and Mechanics ; Passion and Action, of 
Electricity ; the Where, of Geography ; the When, of Chro- 
nology ; Position and Quality, of Sculpture ; Habit and Posi- 
tion, of Painting ; and so each art and science would be found 
to range under one of these singly, or more than one when 
combined. 

The books of "Prior and Post Analytics" originate and 
develop his system of the doctrines and use of the Syllogism. 
They have been the resort of all writers on formal Logic since 
his time, and there has been but little alteration in his method. 
Aristotle established but three figures of the syllogism, the 
fourth being afterward added by Galen. 

In his book of Topics he discusses the subject of Predicables, 
or Classes, and establishes the expression of a predicable to be 
in four ways ; i. e., by genus, differentia, property and accident; 
in these he implies the species, since we have seen that if we 
add the differentia to the genus we obtain the species. 

In his book of Sophisms he states thirteen Fallacies as in- 
cluding all those which can bear a syllogistic form. Six of 
these refer to the words used, and are called Fallacies in dic- 
tione, and seven consist in the matter of the propositions, and 
are called Fallacies extra dictionem. 

The logical works of Aristotle seem to have been providen- 
tially preserved. Transmitted by his disciples from hand to 
hand, they were at length concealed in a vault during one 
hundred and thirty years, until they had mouldered into an 
almost illegible condition. Restored from this condition, 
they came by the fortune of war into the hands of a Poman 
general, and thus were given a second time to the world. 

We cannot pause to notice all the changes attempted in 
Logic and Philosophy from this time until the Christian era. 
After the Peripatetics came Pyrrho of Elis and his Skeptics, 
who seem to have employed Logic to deny the possible attain- 
ment of pure truth. They embodied their system in Ten 
Tropes, or logical rules for the government of mind in the 



192 LOGIC. 

search of truth. Their doubt led to what they termed a sus- 
pension of judgment rather than a positive denial. 

Of the Epicureans and Stoics, it may be said that they 
aimed at the establishment of no Logical system, but rather 
a few tenets in the shape of propositions ; by these, as doc- 
trines, they guided their course. 

The tenets of Epicurus may be comprised in the assertion 
that "whatever is useful, pleasant and delightful is true" 
This is to assert that man's senses and bodily appetites are 
the only test of truth. These have been called his " emo- 
tional criteria." 

The Stoics rejected the categories of Aristotle and adopted 
four of their own, and attained the conclusion that " pain is 
no evil" — a philosophic stretch of the imagination which has 
given its name to an unshrinking endurance of pain and 
evil. 

Very little transpires concerning Roman systems of Logic. 
Although Cicero, Maximus of Tyre and Galen lay claim to 
the title of logicians, the logical system of Aristotle was 
adopted by them all ; Rhetoric became the more valued and 
important study. 

The history of Logic, then, from the time of Aristotle to 
the coming of Christ, is not a history of change, but the 
logic of Aristotle, however unchanged, had been most un- 
worthily used. No longer the guide and test of just reason- 
ing, it became the vehicle of ingenious falsehood, was made 
to support any theory and gave power to its possessor " to 
argue on both sides of any question." To satisfy curiosity it 
established any paradox, and one being made the premiss to 
another, the error was multiplied " in infinite progression un- 
defined." It was not the logical system, but the mind of man, 
which needed purification — not abstract propositions, but the 
matter they contained, which demanded scrutiny. 

We shall see also that the misconception of the sphere of 
Logic was equally fruitful of error long after the establish- 



THE LOGIC OF CHEISTIANITY. 193 

merit of Christianity, and that it has remained for the nine- 
teenth century, notwithstanding the utmost resistance of many 
learned but dogmatic philosophers, to give to Aristotle and 
his system their true place in the domain of science — an in- 
stauration not by one man, a new Organon not the product 
of one teeming brain, but the tribute of Philosophy, induc- 
tive and deductive, to Aristotle, the great founder and framer 
of that system which alone controls the unbridled reason 
and sends pure truth into the channels of usefulness and 
practice. 

But, meanwhile, the coming of Christianity was to produce 
great marvels in the domains both of Logic and Philosophy. 

(57.) The Logic of Christianity. 

The Logic of the Grecian schools had been the guide of 
man's Reason, but now r it was itself to be brought into com- 
panionship with a higher human attribute, Faith. Premisses 
were no longer to be sought by the ordinary means of evi- 
dence, but to be supplied in a new and marvelous manner. 
Christianity combined this new element with Philosophy, and 
taking the art of Logic as the vehicle of its great truths, 
used it in a manner at once beneficial and practical, putting 
an end, as it seemed, to the controversies and paradoxes which 
had beguiled and engaged the Greek and Roman mind. 

By this new tutelage of human reason, Christianity pro- 
duced an immediate and startling change in Philosophy by 
opening the Finite upon which man may use his reason, as 
well as indicating the Mysterious and Infinite to his faith. 

As much as we may despise the Greek systems of specula- 
tive Ethics upon which they employed their nobler Logic, 
we must remember that they were the gropings of men in the 
dark, pursuing a faint glimmer of light in the hope that it 
would lead them into the full sunshine and free air of Truth. 
They had no revelation of intelligible fact or of mystery. 
The efforts of Plato to attain to different degrees of know- 
17 n 



194 LOGIC. 

ledge which he calls " the absolute, the probable, the imper- 
fect," the Politics and Ethics of Aristotle, the bold dicta and 
quiet endurance of the Stoics, the " emotional criteria of 
Truth," propounded by Epicurus, and so much abused by his 
disciples, were all vain attempts to arrive at that knowledge 
which could come to man only by miraculous revelation. 
God vouchsafed no such revelation to them ; it is no cause of 
wonder that they erred greatly without it. 

This, then, was the crowning glory of Christianity, that it 
gave to man pure Truth, and furnished him with a world of 
new facts upon which to reason, of glorious propositions upon 
which to try the powers of his Logic. They furnished him a 
boundless field, with the word of God as a beacon infallible, 
and where reason could not obtain internal or analytic evi- 
dence, resting its judgment on external evidence as a basis. 
God said to man, Believe and ye shall be saved. 

Unlike the Greeks, the Jews had always possessed this 
revelation in a ceremonial and progressive form. Their own 
Scriptures had disclosed to them not only the true story of 
man's origin and fall, but of God's supremacy and his gra- 
cious design of restoration, and their prophets had told them 
with a heavenly Logic of Type and Symbol, premiss upon 
premiss in glorious abundance, of that certain conclusion, the 
advent of the Messiah. 

The " fullness of time " came, and the event fulfilled the 
prophecies, the conclusion completed the premisses. Chris- 
tianity brought philosophic as well as religious light. 

By a strange infatuation, they who had thus awaited His 
coming refused Him when He came; and since He could 
not be the glory of His earthly "people Israel,' 5 He was, in 
a truly philosophic sense, " a light to lighten the Gentiles." 

In three centuries, He had been eagerly embraced by 
heathen Borne, and the Logic of Aristotle, freed from its 
vile and improper uses and used as the propounder of a full 
and pure creed, was applied with great power to the spread 



THE LOGIC OF CHRISTIANITY. 195 

of the Christian religion. Where false premisses had been 
ignorantly used, leading to a false conclusion, or where false 
conclusions had been improperly deduced from true premisses, 
everything for a time was changed. Truth was everywhere 
triumphant, and its reign seemed to be eternal. 

Such was the first influence of Christianity upon Logic. 
Containing in itself nothing repugnant to reason, it gave a 
host of new and glorious truths fresh from the mouth of God ; 
it simply threw away the vague speculations, the unsound 
paradoxes, which had been heretofore used as premisses, and 
took these new truths to reason upon. In the teachings of 
our Saviour and the apostles, it need scarcely be remarked, 
not only that every statement is true, but that every argu- 
ment is valid. 

On the other hand, Logic, turning gladly away from the 
subtleties and absurdities of mythical philosophy, pressed 
forward with ardor in the task of systematizing and promul- 
gating the new doctrines of Christianity. 

In this manner arose the logical systems of the early Chris- 
tian writers and apologists known as " the fathers." There 
is, indeed, error to be found in their uninspired writings, such 
as we should expect in all human productions, but, from Jus- 
tin Martyr to St. Augustine, one object of their writings 
seems to have been the harmonizing of Christian doctrine 
with the Logic of Aristotle, and thus, while they preached 
the truth, to show at once the union and true relation of 
Reason and Faith. How well they succeeded as a class may 
be seen at the present day from the growing interest in their 
writings which is manifested by all who are interested in 
Religion or Philosophy. Never forgetting that they were 
surrounded by enemies and error, one part of their works 
was fiercely controversial, always keeping in view the elen- 
chus, and warily observing an opponent, or rather the many 
opponents who were scrutinizing their deeds and words. 

Where, in the old system of Philosophy, Sensation was the 



196 LOGIC. 

starting-point, and man must evolve philosophy from within 
himself, they established Revelation as the centre and starting- 
point, and would draw, by the same logical formulae, all true 
philosophy from God. From this time Logic was insepara- 
bly connected with theology ; the Church ruled the world. 

The Christian Church had, in its union with the Roman 
empire, a strength and stability from which great philosophic 
results must have sprung ; but just when they were framing 
this glorious system at once of Religion and Philosophy, the 
Roman empire of the West fell under the ruthless attacks of 
the Northern barbarians, and the Church was temporarily 
paralyzed by the shock. For centuries after, the great 
efforts of the Church were directed to the attainment of a 
firm social basis and political power. 

We have already stated the connection between Logic and 
Philosophy. They may be dissociated, but are both then 
useless. Thus, indirectly, Philosophy has exerted such an 
influence upon the uses of Logic that it is important to trace 
the systems with which Logic was combined, and to promul- 
gate which it was used after the establishment of Christian- 
ity. Most of the Christian writers investigated the subject 
of the human reason, and studied the Logic of Aristotle. 

As might be expected, so magical a transformer as Chris- 
tianity was not without fierce philosophic opposition. With 
equal step Skepticism and Heresy advanced. Those who 
were doubters before where only Science was concerned were 
doubly doubters when told of Christian mysteries. 

The representative of the new skeptics was Sextus Empir- 
icus, who lived in the beginning of the third century, and 
who was but a new incarnation of Pyrrho of Elis. Unwill- 
ing to receive, on prima facie evidence, the truth of the new 
revelation, they had fallen back upon the old material, and 
had worked to the same results as the Greek philosophers ; 
they turned their backs on the light — which admits of no 
better proof than the physical light of day — and walked into 



THE LOGIC OF CHRISTIANITY. 197 

the cave of darkness, of doubt and, in a religious view, of 
despair. 

The skepticism of Pyrrho, three hundred years before 
Christ, was consistent and well deduced when compared with 
this, and yet the Greek academicians, we know, had con- 
victed him of absurdity. " Because everything is contra- 
dictory, everything is false." Now, if this be true, the axiom 
itself is false, and so the skeptic, thrown upon the horns of 
a dilemma, must grope again in vain for new proofs of false- 
hood and new certainties of doubt. 

Of the Neo-Platonic, Eclectic or Alexandrian school, the 
object seems to have been to unite the Greek philosophy and 
Oriental dogmatism into one system, but it was a false and 
feeble combination, fated to a speedy and ridiculous end. 

Its metaphysics, as prepared by Plotinus, was the attempt 
by the combination of heathen obscurities to attain to Chris- 
tian light; its theology, as reduced by Iamblichus, was a 
strange retrogradation from the Scriptures, which revealed 
the person and word of God, to the ridiculous deities of the 
Pantheon ; and its Logic, of which the great Porphyry was 
the applier, was an attempt, by the use of the Aristotelian 
system, to establish all these errors, at the expense of the 
fair fame and even of the existence of Logic. 

Nor in the singular application of Christianity to Logic 
must the Gnostics be forgotten. Their name indicated their 
creed; yycoffis, -knowledge, as opposed to faith: naked Logic, 
stripped of its armor, was made again to do duty in the 
ranks of the Prince of Darkness. Gnosticism "took such 
portions of the Gospel as suited its views or struck its fancy, 
but these rays of light they mingled with such a chaos of 
absurdity that the apostles would hardly have recognized 
their own doctrines." * 

The greatest perhaps of the indirect evidences of the truth 
of the Christian religion is that, in spite of the false systems 

* Burton's "Heresies of the Apostolic Age," p. 15, quoted by Neil. 
17* 



198 LOGIC. 

which sprang up to oppose it, it has steadily and mightily 
prevailed ; in its progress it has purified human philosophy 
and unfettered Logic ; but it did not accomplish this without 
fierce contests ; it was to come upon dark days in which it 
was the only glimmer of light — days in which the misuses 
of Logic were no longer to be confined to profane systems or 
heretical creeds. 

Then came the Schoolmen or the so-called Scholastics. 

The first era of Scholasticism was the adoption - of Logic 
as the form and vehicle for Religion, and thus far they were 
in the right path. 

The second phase was the attempt to unite Religion and 
Philosophy, and this produced new champions of Realism. 

The third jmase was an opposition ; Religion and Philoso- 
phy were rudely dissevered, and this produced Nominalism. 

If, now, we separately consider these three phases of the 
Scholastic philosophy, we shall perceive that the first was the 
just and true one, and that the succeeding ones were learn- 
ing which had to be unlearned. 

That part of the Greek system which could be made the 
form and vehicle of religion, as it is of all correct reasoning, 
was only the Logic. To apply that to the service of Faith 
was just the first design of Christianity toward Logic, and 
thus far the Schoolmen were right — indeed, it would seem 
ignorantly right, for while using the forms which constitute 
Logic, they still persisted in calling many other parts of the 
Greek philosophy by the name of Logic, and thus making 
Logic bear the blame which truly belonged to the errors, 
obscurities and absurdities of exploded systems of metaphys- 
ics, theology and morals. 

This is apparent in the works of Alcuin, the contemporary 
and friend of Charlemagne, and especially in his dialogues 
on " Grammar, Rhetoric and Logic." 

Lofty was the simple distinction of St. Anselm that there 
are but two modes of Cognition, Faith and Science, and 



THE LOGIC OF CHRISTIANITY. 199 

grander yet the idea, "that Science begins where Faith 
ends"— in the bosom of God ! 

But let us consider the second and third phases. 

Nominalism and Realism were but the reproduction in 
the ninth century of the old Platonian controversy already 
referred to. Nominal and real were the abstractions of what 
we call respectively universal and particular. 

When I speak of a single man, and point him out, I desig- 
nate a real, existent individual ; when I speak of man as a 
common term, is there a real entity corresponding to the 
word ? The Realists said, Yes ! the Nominalists said, No ! 
it is but a name to indicate numbers. This had been the 
origin of the controversy. 

Plato, with his divine but vague philosophy, had asserted 
that there was a real existence, an archetype in the bosom of 
God corresponding to the name of a class, as man, angel; 
Aristotle, that they were only generalized names from many 
individual abstractions. And thus these great parents of 
Logical Philosophy set the example of wrangling to their 
myriad children of the schools. It is curious to see how 
such a dispute first connected itself with religion. It was 
thus: the question seemed to involve another and a more 
important one, viz. : " What is the foundation of human 
knowledge?" Roscellinus of Compeigne, who lived in the 
eleventh century, was the originator of the new controversy 
in the Middle Ages between the Realists and the Nominal- 
ists. He was a fierce Nominalist ; and as this led to supposed 
heresies, he was an object of persecution on this account. 
As warmly was the cause of realism espoused by William of 
Champeaux, and throughout the schools there was a word- 
war of great fierceness on this subject. 

Passing over the quarrels of the Schoolmen until we reach 
the time of Roger Bacon, and thus neglecting many great 
names in the history of Logical Philosojmy, we are struck 
with the power of his experiments and analyses, and the 



200 LOGIC. 

manifest fact that he deserves the name of the founder of 
Experimental Philosophy — that his " Opus Majus" may justly 
be considered the precursor of the "Novum Organum" of his 
more illustrious namesake, Francis Bacon. 

Disgusted with the categories of Aristotle as trammeling 
an ardent physical scholar who must establish categories for 
himself by experience, he considers experiment, based upon 
constant observation, the only rule for philosophy, and in his 
works in the laboratory and with his pen we discern the first 
dawning of the day of Induction. 

For a while, as was very natural, formal Logic fell into dis- 
repute, and gave way to experiment in physics ; and from 
that day down to our own times, there has been but little 
appreciation or understanding of the art of reasoning, although 
it has been constantly used and constantly ignored. Like 
savages who breathe the invisible air round them and are 
not aware of its existence, so minds of all kinds and calibres 
have used the Logic which they found established as the 
vehicle of thought without knowing where to make their ac- 
knowledgments. 

(58.) The Logic of Experimental Philosophy. 

Now an element seems to have been introduced into phil- 
osophy which till then had been considered unimportant, 
and that was observation and experiment; or, to use the term 
by which we have expressed the methodical and successive 
observations of such phenomena in nature as will lead us to 
general laws, Induction. Aristotle himself had stated the 
value of induction for the discovery of new truth, and men, 
in all ages, had used it as an exercise of common sense in their 
ordinary conduct ; so that it must not be supposed that, in 
any sense, Bacon is its inventor. He only applied it by 
system to natural science. 

Logic, which is the vehicle of truth in its intellectual pass- 
age from premiss to conclusion, had only reasoned upon the 



THE LOGIC OF EXPERIMENTAL PHILOSOPHY. 201 

known and conceded — mainly from some general law to a 
particular example ; now its premisses were to be new truths 
aggregated by experiment ; it was to reason from many par- 
ticular examples to the establishment of a general law. 

Bacon was the early interpreter of Nature, Descartes more 
especially the analyzer of Thought. To each is due an illus- 
trious share of the developments in philosophy. But Bacon 
is the more distinguished because his investigations were 
made in every domain of nature, and his system is at once 
more intelligible and popular on that account. 

The starting-point of Bacon's philosophy was the assertion 
that the universe is a great storehouse of facts, and that it is 
man's duty and interest, and it ought to be his pleasure, to 
explore, discover and understand these facts, not only in their 
isolated characters, but in their relations to each other and 
to the universe itself. His experiments and his use of the 
experiments of others were to enable him to arrive at general 
laws of the universe. Now, corresponding with the world 
around us — that is, the world of nature— there is a world 
within us, the world of Thought. Let either be impaired or 
cease to exist, and in just such a proportion is the other im- 
paired or does it cease to exist. 

To unite them we have sensation and perception, and the 
union is lost if sensation and perception fail. 

The happy union, then, of Thought and Nature, would lead 
man to Truth, and to attain to Truth is his highest aim. It 
will at once be seen that this was the establishment, not of a 
logical, but of a philosophical system. But to proceed : the 
various forms which truth assumes in order to inspire the fac- 
ulties and entice the pursuits of men are called sciences, and 
by an examination of multitudes of these phenomenal facts 
the true definitions of the sciences might be made, their true 
relation determined and a plan of classification formed for 
practical purposes. 

Such, then, very briefly, was the aim of the new experi- 



202 LOGIC. 

mental philosophy — a great restoration which was proposed 
by Bacon in his Instauratio Magna. With it directly Logic 
had but little to do, but that little led men of science into 
errors w r hich remain to the present day. 

Without attempting to enter into the details of the " Great 
Restoration," it will be well to consider some of the steps 
proposed by Bacon as preliminary to it. Finding, in his 
inquiries about facts or phenomena, that they greatly differ 
in importance— that some are simple, others complex, some 
are easy of interpretation, others very difficult — he proposed 
a classification of the instances in which any phenomenon or 
fact occurred, and this should be a sort of value scale of the 
instances in which a special phenomenon occurred. These he 
calls prerogative instances, or those cases of most importance 
to us in interpreting a fact or a series of facts. He has 
stated twenty-seven of these, from which we shall choose six 
as better illustrating their own meaning than it can be done 
in other words. Our purpose is not to use these, but merely 
to indicate their nature and design. 

I. Solitary instances, or those in which two or more objects 
agree or differ in all qualities save one. Thus a rabbit-skin 
and a piece of rough glass, which differ in all other qualities, 
agree in this, that on being excited by a metal they both 
become charged with positive electricity, while two pieces of 
silk ribbon, only differing in color, when thus excited, become 
the one positively and the other negatively electrified. 

II. Forth-showing instances. Under this head range those 
facts or instruments which show forth the quality in question 
in the highest degree, as a galvanic battery in electricity and 
a barometer in pneumatics. 

III. Analogous instances. Those in which are found objects 
bearing a resemblance of purpose or relation, however unlike 
the objects themselves may be. Thus, a camera-obscura is 
analogous to the eye and a system of watermarks to the 
heart. 



THE LOGIC OF EXPERIMENTAL PHILOSOPHY. 203 

IV. Crucial instances. There are two probable meanings 
to the word crucial as here used. It may be the putting 
nature to the torture, the crucifying her, to wring from her 
her secrets, or it may have reference to the wayside crosses 
which at the parting of the roads indicate the true direction 
to the traveler. Franklin's electric kite might be called a 
crucial instance, in the first sense. Such also, in the second, 
was Newton's law of gravitation, a finger-board for ever to 
point to the true direction of investigation and belief con- 
cerning our solar system. 

V. Varying instances (Instantice migr antes). Those pro- 
pensities of bodies which change to a greater or less degree. 
Among these would be included change of form from solid 
to liquid and from liquid to gaseous, and the reverse. 

VI. Companion and hostile instances. Of the first would 
be qualities which usually accompany each other, as heat 
and flame ; of the second, those which are never in conjunc- 
tion or alliance, but seem to repel each other, as the posi- 
tive and negative poles in electricity. 

The other instances, which we cannot stop to mention, are 
designed to exhaust the classification of experiments on facts, 
and to lead to induction ; and here began the danger and dif- 
ficulty; it was here, also, that the syllogism which Bacon 
despised and misunderstood was and always is the only safe 
guide of Philosophy. For, suppose the facts ranging under 
these instances to be established, how many of them will give 
us the right to the establishment of a general law or a dis- 
tinct science? We have seen that, in most sciences, we only 
attain to likelihood. On account of human ignorance, the 
process has been this: we first observe a few facts; we 
then adopt a hypothesis based upon them — i. e., jump at 
the general law — simply in order to make a nidus for our 
accumulating facts, and thus proceed to verify — if the new 
facts will verify — our proposed theory. The tendency of 
man's mind is so great, how T ever, to repose upon a darling 



204 LOGIC. 

hypothesis, even if it be unsound, and rather to seek, like an 
advocate, for such facts and statements as will support it, 
than to look for just proof, and in the absence of such to dis- 
card it, that induction has often led to grievous error. Many 
a student has learned on hypothesis some part of Natural 
Science, and when he had just mastered it has been obliged 
to discard it for another. 

In the consideration of Judgment, Bacon has given special 
attention to the fallacies which assail the mind of man. 
These he calls idols of the intellect, and in almost every case, 
since they are contained in false judgments, they belong to 
the class of material fallacies. But all these idols occasion- 
ally assume the garb of logical fallacies. 

These idols, or eiowXa, which Bacon calls " the deepest fal- 
lacies of the human mind," are the sources of error which 
assail men in their investigations in Philosophy, and which 
" must be renounced, and the intellect wholly freed and puri- 
fied therefrom," before we can hope for healthful progress. 
By the word idol Bacon means the prejudice which stands 
in our way of receiving truth and the bias of the mind from 
which such prejudices arise. 

But these idola will most clearly explain themselves ; they 
are of four classes — Idola Tribus, Idola Specus, Idola Fori, 
Idola Theatri ; and with reference to these an author of his 
own time remarks : " The temple which he purified was not 
that of nature itself, but the temple of the Mind; in its 
innermost sanctuary were all the idols which he overthrew." 

1. The idols of the tribe are those which are imposed upon 
the understanding by the general nature of mankind ; in 
other words, they belong to the human tribe, in its universal 
comprehension. Thus, he asserts that men, as men, are 
quicker to be moved by affirmative and active events than by 
negative and 'privative, though in justice they should be moved 
by both. To illustrate this, he tells the story of the Greek 
who was shown in Neptune's temple the votive pictures of 



LOGIC OF EXPERIMENTAL PHILOSOPHY. 205 

those who had escaped shipwreck ; and when asked if he did 
not now acknowledge his divinity, said: "Show me first 
where those are painted who paid their vows and were then 
shipwrecked." 

2. The idols of the den or cave spring from the nature of 
each particular man, and groAV out of his peculiar features 
both of mind and body ; these may also be fostered or devel- 
oped by education, custom or accident. The name is sug- 
gested by fancying the confusion and error of a man being 
brought out of a dark den or cave into the full light and 
glory of nature. This finds its counterpart in the world of 
philosophy, where men only emerge from the den of their 
minds to find confusion and disorder in the beautiful universe 
of God. 

3. The idols of the market are errors which grow out of 
words and communication, such as are the pass-words and 
common coin of conversation and intercourse in the market- 
place ; and they imply, like the idols of the tribe, a social 
organization, but on a much more limited scale. Instead of 
being universal with men, they are errors which belong to a 
small circle, like a crowd in a market-place, moved, at the 
sound of an orator's words, by a common impulsion of pre- 
judice, passion or other emotion. These idols are causes of 
the greatest disturbance, as they are immediately connected 
with the naming of things, " for words are generally given 
according to vulgar conception, and divide things by such 
differences as the common people are capable of; but when 
a more acute understanding or a more careful observation 
would distinguish things, better words murmur against it." 

Thus, many words in our every-day use convey no definite 
meaning to the mind, but have, in their very indefiniteness, so 
many shades of meaning that they are a constant cause of ver- 
bal fallacy. As special reference has been made to such words 
in the chapter on Fallacies (X.), it will only be necessary 
to mention a few such to illustrate the idols of the market- 
18 



206 LOGIC. 

place ; such is the word republic, which we have been apt to 
confound with democracy ; Liberty means either freedom or 
license, as its champions wish, and taste and beauty have as 
many forms as there are eyes to see or imaginations to indulge. 

The last of the sources of error enumerated among the 
idols of Bacon are the idols of the theatre. These he distin- 
guishes from the others as perhaps of more social power and 
influence. Of these he says, "They are superinduced by 
false theories or philosophies, and the perverted laws of dem- 
onstration." They are comprehended under three heads, 
Partisanship, Fashion and Authority. 

Partisanship is the generic name under which are found 
factions in j)olitics and in religion, and under whose influence 
wars of creed and caste have so often desolated the world. 

Fashion is a kind of partisanship which, however, has few 
opponents and no great rivalries, but which pervades society 
from high to low. We do not refer to its simple sway in 
dress, equipage and social life, but to its more comprehensive 
dominion over all the works and thoughts of man, over art, 
science, religion. Great masses of men are herded like cat- 
tle and driven willingly in the train of this all-swaying Fash- 
ion, resting their happiness here and their hopes in an eter- 
nal future upon the dictum of Fashion. 

As Fashion partakes of the nature of Partisanship, so is 
Authority strengthened by an alliance with both. This eon-. 
sists in blind obedience to an existing control and reliance 
upon it without the use of our own judgment. 

As God, who has given man Reason, has made some things 
higher than that reason, but nothing repugnant to it, every 
theory of authority in Church, in State or in general philoso- 
phy is, of right,. to be examined by our reason before we can 
accord to it our belief. Reliance upon authority, without a 
due understanding of its claims, is to treat our own moral 
constitution with injustice, and to stop the wheels of healthful 
progress both of individuals and societies. 



LOGIC OF EXPERIMENTAL PHILOSOPHY. 207 

In reviewing these error-sources it is scarcely necessary to 
remark that it is the abuse and not the use of our words and 
associations which lead to them. 

Thus, the idols of the tribe would not be false and deceit- 
ful if man should concur universally and everywhere in just 
and truthful opinions, nor would the den darken men's minds 
to the true light if they were capable of carrying into their 
meditation the true elements of combination and just views 
of the objects in the universe around them. Heraclitus has 
told us "that men seek the sciences in their own narrow 
worlds and not in the wide one." Such is the influence, but 
not the necessary consequence, of the den. 

So it is easy to avoid the errors which grow out of ambig- 
uous words, such as those which mark the idols of the market, 
by demanding just definitions, and when such cannot be given 
either agreeing for argument's sake upon one which is not j ust, 
or declining to argue at all where the very question is in- 
volved in obscurity. 

We may observe, concerning the idols of the theatre, that 
partisanship has its good as well as its evil character, and 
that to championize the right is noble and just ; it is, how- 
ever, even in such a cause that its tendency is to extremes. 

So fashion, crowds of whose votaries are miserable and self- 
tortured, is incident to man's social character, and is produc- 
tive to those who use it aright of method and comfort and 
success. Although fashion has done much evil, it could not 
be spared in our social or intellectual systems. Nor must 
Aidhority, however formidable the name, be accounted of 
slight importance, for under just authority are ranged obe- 
dience, order and ivholesome discipline; without it government 
would be anarchy, and education would be a curse instead of 
a blessing. It is the time-honored abuse of it which de- 
mands our dislike and resistance. 

Beyond a few and very erroneous allusions to the Logic 



208 LOGIC. 

of Aristotle, Bacon and his immediate successors did very 
little for it as a science. 

Hobbes seems to have just views of the syllogism, as " the 
instrument of demonstration," but carried his investigations, 
his written ones at least, very little beyond such a state- 
ment. 

Resting upon the basis of the Baconian philosophy, the 
thinkers of the seventeenth and eighteenth centuries seem to 
have neglected the art of reasoning for the subject-matter about 
which we reason, and thus to have entirely confounded Logic 
with the art of thinking. For this they had the authority 
of their great master, Bacon, who, in his "Advancement of 
Learning," has divided the Art of Judgment into Induction 
and the Syllogism ; and has classified as four kinds of demon- 
stration : 1. That by immediate consent and common no- 
tions ; 2. By Induction ; 3. By Syllogism ; and 4. By Con- 
gruity. The error of this classification is at once apparent 
to us. 

Indeed, it may justly be said that, in everything pertaining 
to Logic in its proper meaning, Lord Bacon is entirely at 
fault, while in everything which bears upon Experimental 
Philosophy he is great beyond any competitors, for he is its 
founder ; and as a few words have shown that all induction 
must be brought to the syllogism to verify and test the laws 
at which we arrive, his philosophy can be easily disconnected 
from his Logic, and the faults of the latter exert no evil in- 
fluence over the excellences of the former. 

Many logicians in England, France and Germany followed 
in the steps of Bacon in the seventeenth century, attempting 
to unite Logic and Experimental Philosophy in a manner 
which was injurious to the former. 

Locke, misunderstanding the syllogism, as Lord Bacon had 
done, discards it from his system, and bases his views of the 
understanding on two sources by which ideas enter the mind, 
viz., Sensation and Reflection. But to show how so great a 



LOGIC IN THE LATEST PERIOD. 209 

thinker rebukes himself, he states reasoning to consist of four 
parts: 1st. Finding proofs; 2d. Arranging them; 3d. Show- 
ing their connection ; and 4th. Employing them correctly. 

Now, what is all this but, 1st. Finding middle terms by 
which to establish premisses ; 2d. Stating syllogisms ; and 
4th. Combining arguments ? As for the 3d, that is included 
in the 2d, for they cannot be arranged without their connec- 
tion being manifest. 

Leibnitz, in Germany, seems to have thrown light upon 
the theories of Descartes, and to have elucidated also many 
things in Locke. 

Milton has been called the most learned man of his age ; 
he vindicated this opinion by writing upon almost every sub- 
ject within the range of knowledge, and in most cases w T rit- 
ing well. We are not, therefore, astonished to find that he 
has written a work on Logic. It is in Latin, and seems to be 
very little known. In that he adheres to much of the Aris- 
totelian doctrine, and specially championizes Peter Ramus, 
the logical Martyr. He divides Logic, which he calls the 
chief of Arts, into two kinds — Natural, i. e., the faculty of 
reason in the human mind ; and Artificial, i. e., rules for 
directing the operations of that faculty. But even Milton 
erred in stating that " it belongs to Logic to lead us from uni- 
versal to particulars," which would limit the Syllogism to 
Deductive reasoning. 

In this state of confusion Logic existed until the new rise 
of Philosophy in the eighteenth century, the source of which 
was the continent of Europe rather than England. 

(59.) Logic in the- Eighteenth and Nineteenth Centuries. 

But little remains to be said in order to complete this brief 
sketch of the History of Logic. Even to mention the names 
of the principal writers who have sprung up under the im- 
pulse of the Baconian philosophy from that time to the pres- 
ent would occupy more space than we can give, and to dis- 
18 * 



210 LOGIC. 

cuss their metaphysical works would in this connection be 
difficult and improbable. 

The logicians of the eighteenth century seem to have bent 
their energies to the task of classifying the science, of making 
such a logical arrangement as would make much labor un- 
necessary and find for each its true niche in the temple of 
Truth. 

In England, Dr. Isaac Watts published a treatise on 
" Logic, or Eight Use of the Reason," which is a compound 
of Logic and Philosophy alike injurious to both. Selecting 
a few tenets from Aristotle, from Lord Bacon and from the 
Schoolmen, he has endeavored to harmonize them. In an- 
other of his volumes, " The Improvement of the Mind," he 
has moved upon surer ground and with much better success. 

Bishop Berkeley wrote the " Principles of Human Know- 
ledge" — a work of profound thought and excellent reasoning ; 
and Bishop Butler has exemplified the correct use and appli- 
cation of Logic in his famous treatise on the "Analogy of 
Religion." 

France has also produced in the eighteenth century many 
fine logical minds who have devoted themselves to science 
specially in attempts at classification ; among these were 
D'Alembert, Diderot and their coadjutors, known as the 
Encyclopaedists, who, in the eighteenth century, startled the 
world not less by their methodical arrangement of the sciences 
than by the skepticism which their studies induced, and the 
atheism or denial of God's existence which took the place 
of doubt. 

It would be impossible in a treatise of this kind to do more 
than simply refer to the present writers on Logic and the 
present condition of the science. 

Archbishop Whately has renewed the Logic of Aristotle 
in its pristine vigor and placed it in its true position as the 
only sure guide or Art of Reasoning. Many English writers 
have differed from him, some in his conception of the mean- 



OF CATEGORIES AND CLASSIFICATION. 211 

ing and scope of Logic itself, and others as to the extent to 
which the Aristotelian system may be carried. 

Of the first may be mentioned Mr. J. S. Mill, whose work, 
according to the view we have taken, may fitlier be called 
"an encyclopaedia of philosophic tenets connected with, or 
resulting from, the Science of Logic."* 

Of the second are Sir William Hamilton and Mr. Augus- 
tus de Morgan, who would develop more than four categori- 
cal propositions and establish what we have called the " New 
Analytic," and yet they differ from each other in their estab- 
lishment. Hamilton, the most distinguished philosopher of 
his age, has numerous followers, among whom are Thomson, 
who has reproduced the Hamiltonian Logic, in an abridged 
form, in a small volume called the Laws of Thought. 

The most important changes, however, in the applications 
of Logic to science, are to be found, as has been said, in the 
subject of Categories and Classification, and to this, in illus- 
tration of the later movements of the science, we shall now 
give a few words. It will be at once perceived that the 
object is to reach a summum genus under which all the 
sciences may range, and then by a logical tree of division to 
place all the lower classes and their co-ordinate species in 
their proper places. In any less general classification it is 
evident that the principle of classification will be changed 
for the different sciences. 

(60.) Of Categories and Classification. 
This is a part of the duty of Method. 
The Categories of Aristotle, which have already been ex- 
plained, may be considered the basis of the classification of 
the sciences ; for although there has been, in former times, 
much dispute concerning their true reference — that is, whether 
it be to words or things or conceptions — it is now allowed that, 
imperfect as they are, they are designed to apply to the summa 
* Neil's Art of Reasoning, p. 234. 



212 



LOGIC. 



genera under which all things which are named may range 
themselves. This establishment of proper summa genera, then, 
is the true start-point of classification. 

Many writers have simplified these categories mainly by 
reducing the number. The schools of Pythagoras, Plato 
and Epictetus had each its corresponding list or table ; Locke 
wrote three, viz.: Physiea, Praetiea and Semeiotica, or, as 
they have been translated, Substance, Modes and Relations ; 
Hume, two, viz. : Ideas and Impressions. 

Among German philosophers and logicians, Kant holds the 
highest place. His views are principally set forth in his 
Critique of Pure Reason. He established as an instrument 
for a pure science of nature the following categories, logical 
and transcendental : 

Logical. Transcendental. 

C Universal. Unity. 

I. Quantity. -< Particular. Plurality. 

(. Singular. Totality. 

f Affirmation. Reality. 

II. Quality. •< Negative. Negation. 

V. Indefinite. Limitation, 

C Categorical. Substance. 

HI. Relation. ■< Hypothetical. Cause. 

(_ Disjunctive. Reciprocity. 

C Problematical. Possibility. 

IV. Modality. ■< Assertory. Necessity. 

(_ Apodictic. Existence. 

Under these twelve categories all forms of our sensible 
experience may be brought. This was only part of a system 
of philosophy, including, besides Logic, aesthetics and met- 
aphysics. 

But these are manifestly none of them of that practical 
form and character which is desirable for useful reference, 
and hence it has been the aim of later writers, especially 
upon Metaphysics and Logic, to write out tables of classifi- 
cation which should comprise and methodize all forms of 



OF CATEGORIES AND CLASSIFICATION. 213 

human science. To classify palpable, tangible objects is to 
arrange them in groups according to a certain method, and 
that method will usually be based first upon the great divis- 
ion of kingdoms, and afterward upon the relation of species 
to genus. 

If we reflect for a moment upon the innumerable forms 
of life and existence in the three great kingdoms, Animal, 
Vegetable and Mineral, we shall at once be struck with the 
difficulty and labor of a just and adequate classification ; and 
yet, strange as it may seem, true progress in any of these 
branches has but kept pace with such a classification, the 
naming and placing of a minute species in its proper place 
being the necessary way of fixing it there for ever. 

It has already been said that the basis of physical classifi- 
cation is the establishment of the summum genus, and that 
the rules of logical division must determine all the subaltern 
genera and species. This must serve us for the classification 
of the known and determined, but in the world of Theory 
another mode may with propriety be adopted : it is the classi- 
fication by series, investigated by Comte. It consists in 
selecting some particular phenomenon the laws of which are 
to be investigated, and then ranging the various objects which 
sustain a relation to it in a nearness proportional to that 
relation. 

With this subject of classification scientific nomenclature is 
immediately connected, and it will appear how important this 
must be regarded when we consider that the value of the 
classification will depend upon the names of the different 
classes, as to their precision or total want of ambiguity, their 
completeness or expressing the whole of the class specified, and 
their expressiveness in denoting the properties of the object and 
the reason of its classification. Thus, in Chemistry, a law of 
nomenclature has been formed, based, indeed, upon some 
unfortunate beginnings which have been allowed to remain 
but very systematic and universal in its reception. 



214 LOGIC. 

But the high aim of metaphysical philosophers to smooth 
the paths of Logic has been, not the classification of one sci- 
ence, but the analysis and classification of universal Science, 
the establishment of a complete table in which all human in- 
vestigation should find its place and link itself to the great 
mind of all ages in its study of all topics within its sensual or 
intellectual range. 

It will not be attempted to give a history of classification, 
nor to prepare or copy a complete table of any previous 
author, but rather to indicate the manner in which it has 
been done, with a general reflection upon the results attained. 
Classification, to be logical and just, must be made after cer- 
tain investigations which are necessary to determine the true 
class of the object in question. This will be done in Physics 
by formal analysis, such as the organic analysis in Chemistry, 
and in the exact sciences by the application of the principles 
of demonstrative proof. 

Passing by, only because our limits do not permit their 
consideration, the system of Bacon, which was adopted by 
the French encyclopaedists of the last century, and the de- 
tails of the system of Locke, we come down to our own times 
before we find any definite attempt to supply the want. An 
eminent Scotch writer, as he reviewed the efforts of previous 
philosophers to classify human knowledge, asserted that it 
was an impossible task, and so, from its magnitude, it would 
fairly seem. 

Nothing daunted by such an assertion, Coleridge suggested 
the plan of classification which was adopted in the arrange- 
ment of the English "Encyclopaedia MetropoKtana," but 
which he found to require, after he had exhausted his cate- 
gories, an additional category of "Miscellaneous" species — 
the unfortunate subalterns which had no summum genus 
under which to range themselves. 

Among the curious but highly philosophic remains of 
Jeremy Bentham is a proposed system of scientific classifica- 



OF CATEGORIES AND CLASSIFICATION. 215 

tion ; but, like his other works, it is only a storehouse of 
theory from which less gifted but more practical men draw 
capital for constant use. 

All the more modern writers agree in considering the sys- 
tem of Ampere the most correct and useful. It is based upon 
the two categories of mind and matter, and under these it ex- 
pands into a very great number of subordinate sciences, many 
of which, it must be said, are created, i. e., in name, to fill up 
gaps which would spoil the symmetry of his table. 

It is not our purpose to write out his table in full ; it would 
be out of place in a text-book, as it could only be examined, 
not studied ; but we will form a tree of one or two of his sub- 
jects to illustrate his plan and indicate its truthfulness and 
use. 

His First Table contains : 

(Kingdoms.) 
/ Cosmological sciences, \ / Zoological sciences, \ 

\ i. e., 'pertaining to matter. J \ i. e., pertaining to mind. ) 



Cosmologies proper. Physiologies. Noologics Social sciences. 

| proper. 



Mathematics. Physics. Mat. sciences. Med. sciences. Philosophies, etc. Ethnology. 

I III etc. 

Geometry, etc. etc. etc. etc. | 

| etc. 

Elementary geometry, etc. 

I 

Synthetical and analytical geometry, 
etc. 

Of these there are several tables and more than a hundred 
branches. In thus indicating rather than writing out in full 
the tables of Ampere, we spare the student the reading, in 
place, of many names unknown to our ordinary scientific 
studies, such as Dialegmatics, Eleutlierotechnics, Technesthetics, 
while we present to him what is alone our present purpose, 
the theory and principle of classification. 



216 LOGIC. 

The chief merit of his tables, which he spent his life in con- 
structing, seems to be that there are no cross divisions — that 
no subordinate science lies out of its own class or laps over 
into another — errors which rendered Bacon's system worthless, 
and which caused Bentham to abandon his great idea and 
leave it in its inchoate form. 

Auguste Cointe, who has given to the world, in his Cours 
de la Philosophie Positive, his views of philosophy, did not 
attempt so much to classify science as to determine the true 
relation between general science and positive science — to make 
positive science more general in its application and general 
science more practical and positive. This has been his life- 
work. There is much of his work which bears indirectly but 
dangerously upon religious belief, and there is an elaborate 
description of the historical progress of positive science 
through what he calls the mystical and metaphysical eras to 
the positive. 

To explain more clearly his view of this positive era, it is 
that in which the mysticism or mythology of ancient and early 
times, as well as the crude metaphysical notions of the Middle 
Ages which found their issue in astrology and magic, are 
swept away by the light of modern free thought and investi- 
gation, and in their place are substituted the laws of creation — 
laws which regulate its origin, its progress and its destiny. 
There are six positive sciences which include everything that 
can be known. These are Mathematics, Astronomy, Physics, 
Chemistry, Biology and Sociology. 

But it is not within our scope to explain his philosophy ; 
we have only to do with its Logic, and this is found in his 
classification. 

The subject of classification is yet open, and will become, 
without doubt, clearer and more practical as science advances 
to the discovery of the proximate laws of creation. 



CONCLUSION. 217 

(61.) Conclusion. 

From the foregoing investigation of the art of Reasoning, 
we may pause a moment at the end to reflect upon its real 
value and importance. If Logic is really the art which con- 
trols and guides the reason in its workings, and without 
which we can attain to no truth upon which the reason is 
exercised, it is surely worthy of a high place in the catalogue 
of elementary studies, and the statement and adoption of its 
laws must be considered of the first importance. 

And, above all, should it be placed upon its own founda- 
tion, and dissociated from any other sciences which either rob 
it of its own identity or use it without acknowledging its 
office. 

19 



APPENDIX. 

EXAMPLES FOB PRAXIS. 

Logical praxis consists in the application of the rules of 
Logic as a test of all the forms of argument. The following 
examples for praxis are designed to give ease and logical 
quickness of detection to the student. They comprise illus- 
trations of all kinds and forms of argument — regular syllo- 
gisms, irregular and inverted arguments, compound argu- 
ments, fallacies of every kind, curious propositions, examples 
of the processes of generalization and division, amphibolous 
sentences, etc., etc. A certain number of these should be 
given to the student, as an exercise with each lesson, upon the 
review of the subject. He should be required to state what 
each is in its present form — if & fallacy, of what kind; if a 
logical fallacy, to write it out by symbols and thus to expose 
its invalidity ; if an inverted argument, to put it in the true 
order of sequence of premiss and conclusion ; if an entliymeme, 
to supply the suppressed premiss ; if in an imperfect mood, to 
reduce it to one of the perfect moods of the first figure, — in a 
word, to show by this practice the truth of the assertion made 
at the beginning of this book, and steadily kept in view 
throughout the work, that every valid argument, whatever 
its form, may be brought directly to the dictum of Aristotle 
as the final test of argument. 

In a few of the more difficult examples, to guide the student, 
a reference has been made to the page on which their type 
may be found. Some selected arguments from the Latin 
authors, generally read in the schools, haVe been added, as 
of interest to the classical student. 
218 



EXAMPLES FOR PRAXIS. 219 

1. Jupiter, Saturn, Venus, Earth, etc. move round the sun 
in ellipses ; these are all planets ; therefore all planets move 
round the sun in ellipses. 

2. Induction is the only true science of reasoning ; Syllo- 
gistic Logic is not induction ; therefore Syllogistic Logic is 
not a true science of reasoning. 

3. No one is good who commits sin ; all men commit sin ; 
therefore there is none good except God. 

4. A story is not to be believed the reporters of which give 
contradictory accounts of it ; the story of Napoleon's life is 
of this kind ; therefore it is not to be believed. 

5. Every one desires happiness ; virtue is happiness ; there- 
fore every one desires virtue. 

6. No evil should be allowed that good may result ; all 
punishment is an evil ; therefore no punishment should be 
allowed. 

7. Those who are over- credulous should not be believed ; 
the ancient historians w r ere over-credulous; therefore we 
should believe nothing they say. 

8. An American citizen should be free ; I am an American 
citizen; therefore I should be allowed to do whatever I 
please. 

9. The duke yet lives that Henry shall depose, (v. p. 154.) 

10. All the peaches in this field are worth one hundred 
dollars ; this is one of the peaches in this field ; therefore it 
is worth one hundred dollars. 

11. Ought we to act from expediency as a motive? 

12. Ought not children to obey their parents ? 

13. A designing character is not worthy of trust .; therefore 
I do not trust engravers. 

14. All good men are beloved by their associates ; this man 
is beloved by his ; therefore he must be good. 

15. Pallas ne exurere classem 

Argivum atque ipsos, potuit submergere ponti. 



220 APPENDIX. 

Ast ego que Divum inceclo regina Jovisque 
Et soror et conjux, una cum gente tot annos 
Bella gero. 

16. Happiness consists in obedience to the Divine Laws ; 
this obedience is virtuous conduct ; virtuous conduct is the 
subordination of the inferior to the superior in our nature ; 
this subordination is induced by self-control ; therefore happi- 
ness is the result of self-control. 

17. Crime is a violation of the laws of our country; piracy 
is crime ; this man belongs to a band of lawless men, and 
this band has been taken in the very deed of piracy ; there- 
fore he has violated the laws of his country. 

18. He that is of God heareth my words ; ye therefore hear 
them not, because ye are not of God. 

19. We must do one of three things — go back, stand still, 
or go forward ; we cannot go back or stand still ; therefore 
we must go forward. 

20. " Ay, in the catalogue ye go for men — 

As hounds and greyhounds, mongrels, spaniels, curs, 
Shoughs, water-rugs and demi-wolves are called . 
All by the name of Dogs." 

21. All that glitters is not gold ; tinsel glitters ; therefore 
it is not gold. 

22. Warm countries alone produce wine ; therefore Spain 
produces wine. 

23. Quo melior servo quo liberior sit avarus, 
In triviis fixum, cum se demit tit ob assem, 

Non video. Nam qui cupiet, metuet quoque porro 
Qui metuens vivit, liber mihi non erit unquam. 
Or, The fearful man is not free ; the miser is fearful ; there- 
fore the miser is not free. — Hor. Ep. 1, 16. 

' The following strong eulogium of Logic is an argument of 
the schoolmen, who called it " The Divine art ; the eye of the 
Intellect ; the art of arts ; the science of sciences ; the bulwark 
of philosophy " : 



EXAMPLES FOR PRAXIS. 221 

24. Utque supra iEthereos sol aureus emicat ignes, 
Sic artes inter prominet hsec Logica ; 

Quid ? Logica superat solem ; sol namque, diurno 
Tempore dat lucem, nocte sed hancce negat; 
At Logicse sidus nunquam occidit ; istud in ipsis 
Tarn tenebris splendet, quam redeunte die. 
Cum hoc, ergo propter hoc, a form of the non causa pro 
causa, is broadly illustrated by the following : 

25. The encroachment of the sea upon that bank upon the 
coast of Kent known as the Goodwin Sands, rendering it very 
dangerous to navigation, led to the appointment of a com- 
mittee of parliament to inquire into the subject. The com- 
mittee went down, and examined, among other witnesses, an 
old man, who, when asked what he regarded as the cause of 
this encroachment, replied, after some minutes' thought, that 
he did not know, unless it had something to do with Tenter- 
den steeple, as he remembered nothing of the kind before 
they began to build that steeple, but it had been steadily 
growing worse ever since. 

26. Horses are stronger than men ; elephants are stronger 
than horses ; therefore elephants are stronger than men. 

27. Men need the restraints of government, because they 
have vicious propensities. 

28. Unjust laws endanger the stability of government, be- 
cause ( ) ; laws which enslave man's conscience are un- 
just because ( ) ; therefore laws which restrain the free- 
dom of conscience endanger the stability of government. 

29. If we suppose the telegraphic connection from London 
to be made around the world, and the transmission to be 
instantaneous, then a message starting from London at 12 
o'clock to-day would reach London at 12 o'clock yesterday. 

30. If men are to be punished hereafter, God must be the 
punisher ; if God be the punisher, the punishment must be 
just ; if the punishment is just, the punished must be guilty ; 
if they are guilty, they could have acted otherwise ; if they 

19* 



222 APPENDIX. 

could have acted otherwise, they were free agents ; therefore, 
if men are liable to punishment in another world, they must 
be free agents. 

31. This' medicine cured a very difficult case of disease ; 
therefore it will cure every disease. 

32. Among the most bitter persecutions known to history 
were those of the French Revolution ; therefore they must 
have been religious persecutions. 

33. Testimony is likely to be false ; the existence of the 
Pyramids depends on testimony ; therefore we may doubt 
whether there are pyramids in Egypt. 

34. No man can perform impossibilities ; a miracle is an 
impossibility ; therefore no man can perform a miracle. 

35. With God all things are possible. 

36. No man can do these miracles which thou doest, ex- 
cept God be with him. 

37. Si testibus credendum sit contra argumenta, sufficit, 
tantum judicem esse non surdum. — Baco?i's Antitheta. 

38. Hsec, si displicui, fuerint solatia nobis ; 

Hsec fuerint nobis prsemia, si placui. — Martial. 

39. From the existence of bad morals springs the making 
of good laws ; from good laws arises the safety of the com- 
monwealth ; from the safety of the commonwealth all social 
good things flow ; therefore from the existence of bad morals 
come all good things to society. 

40. Si saperem odissem jure sorores, 
Numina cultori perniciosa suo, 

At nunc (tanta nieo comes est iusania morbo), 
Saxa memor refero rursas ad icta pedem. — Ovid. 

41. Csesar oppressit patriam ; Tullius non oppressit patriam ; 
ergo ( ). 

42. Una Eurusque ; notusque ruunt, creberque procellis, 
Africus. 

43. For whom he did foreknow, he did also predestinate 



EXAMPLES FOR PRAXIS. 223 

to be conformed to the image of his Son ; that he might be 
the first born among many brethren. Moreover, whom he 
did predestinate them he also called; -and whom he called 
them he also justified ; and whom he justified them he also 
glorified. Horn. viii. 29, 30. 

44. When the sun is in Cancer, it is summer ; it is now 
summer ; therefore ( ). 

45. All persecution for conscience' sake is unpleasing to 
God, because it is injustice. 

46. Genius must join with study to make a great man; 
this man will never be great, for, though he has genius, he 
cannot study. 

47. No man can serve two masters. Ye cannot serve 

God and mammon. 

48. Pride and innocence are incompatible. The angels 
are innocent ; therefore ( ). 

49. In this life we must either obey our vicious inclinations 
or resist them ; if we obey them, we shall have sin and sorrow; 
if we resist them, we shall have pain and labor ; therefore we 
cannot be free from trouble in this life. 

50. This doctrine cannot be proved from the Gospels ; nor 
from the Acts of the Apostles ; nor from Epistles ; nor from 
the Revelation of St. John; therefore it cannot be proved 
from the New Testament, (v. p. 175.) 

51. It is a sin to kill a man ; a murderer is a man ; there- 
fore he should not be hanged. 



These examples may be increased at the pleasure of the 
teacher. The author would suggest that it would be well for 
students, in their readings both of verse and prose, and in 
their classical studies as well as in English, to cultivate a 
habit of marking the different logical forms of discourse. It 
would soon become a pleasant pastime, as well as a profitable 
lesson. 






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